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\(A,ĐKXĐ:x;y\ge0\)
\(A=\sqrt{xy}-2\sqrt{y}-5\sqrt{x}+10\)
\(=\sqrt{y}\left(\sqrt{x}-2\right)-5\left(\sqrt{x}-2\right)\)
\(=\left(\sqrt{x}-2\right)\left(\sqrt{y}-5\right)\)
\(ĐKXĐ:x;y\ge0\)
\(B=a\sqrt{x}+b\sqrt{y}-\sqrt{xy}-ab\)
\(=\left(a\sqrt{x}-\sqrt{xy}\right)+\left(b\sqrt{y}-ab\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)+b\left(\sqrt{y}-a\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\left(a-\sqrt{y}\right)\left(\sqrt{x}-b\right)\)
a) 2a−4b=2(a−2b)2a−4b=2(a−2b)
c) 2ax−2ay+2a=2a(x−y+1)2ax−2ay+2a=2a(x−y+1)
e) 3xy(x−4)−9x(4−x)=3x(x−4)(y+3)3xy(x−4)−9x(4−x)=3x(x−4)(y+3)
b,d xem lại đề
\(x\sqrt{x}+4x-12\sqrt{x}-27\)
\(=\left(x\sqrt{x}-27\right)+\left(4x-12\sqrt{x}\right)\)
\(=\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9\right)+4\sqrt{x}\left(\sqrt{x}-3\right)\)
\(=\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9+4\sqrt{x}\right)\)
\(=\left(\sqrt{x}-3\right)\left(x+7\sqrt{x}+9\right)\)
a, \(\sqrt{a^2-b^2}-\sqrt{a^3+b^3}\)
\(=\sqrt{\left(a+b\right)\left(a-b\right)}-\sqrt{\left(a+b\right)\left(a^2-ab+b^2\right)}\)
\(=\sqrt{a+b}\left(\sqrt{a-b}-\sqrt{a^2-ab+b^2}\right)\)
\(\text{a)}x\sqrt{x}+\sqrt{x}-x-1\)
\(=\left(x\sqrt{x}+\sqrt{x}\right)-\left(x+1\right)\)
\(=\sqrt{x}\left(x+1\right)-\left(x+1\right)\)
\(=\left(x+1\right)\left(\sqrt{x}-1\right)\)
\(\text{b)}\sqrt{ab}+2\sqrt{a}+3\sqrt{b}+6\)
\(=\left(\sqrt{ab}+2\sqrt{a}\right)+\left(3\sqrt{b}+6\right)\)
\(=\sqrt{a}\left(\sqrt{b}+2\right)+3\left(\sqrt{b}+2\right)\)
\(=\left(\sqrt{b}+2\right)\left(\sqrt{a}+3\right)\)
\(\text{c)}\left(1+\sqrt{x}\right)^2-4\sqrt{x}\)
\(=\left(1+\sqrt{x}\right)^2-\left(2\sqrt{\sqrt{x}}\right)^2\)
\(=\left(1+\sqrt{x}+2\sqrt{\sqrt{x}}\right)\left(1+\sqrt{x}-2\sqrt{\sqrt{x}}\right)\)
\(\text{d)}\sqrt{ab}-\sqrt{a}-\sqrt{b}+1\)
\(=\left(\sqrt{ab}-\sqrt{a}\right)-\left(\sqrt{b}-1\right)\)
\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)
\(=\left(\sqrt{b}-1\right)\left(\sqrt{a}-1\right)\)
\(\text{e)}a+\sqrt{a}+2\sqrt{ab}+2\sqrt{b}\)
\(=\left(a+\sqrt{a}\right)+\left(2\sqrt{ab}+2\sqrt{b}\right)\)
\(=\left[\left(\sqrt{a}\right)^2+\sqrt{a}\right]+\left(2\sqrt{ab}+2\sqrt{b}\right)\)
\(=\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)\)
\(=\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\sqrt{b}\right)\)
\(\text{f)}x-2\sqrt{x-1}-a^2\)
\(=\left(\sqrt{x-2}\right)^2\left(\sqrt{\sqrt{x-1}}\right)^2-a^2\)
\(=\left(\sqrt{x-2}\sqrt{\sqrt{x-1}}\right)^2-a^2\)
\(=\left(\sqrt{x-2\sqrt{x-1}}\right)^2-a^2\)
\(=\left(\sqrt{x-2\sqrt{x-1}}+a\right)\left(\sqrt{x-2\sqrt{x-1}}-a\right)\)
a) \(x-2\sqrt{x-1}-4=\left(x-1\right)-2\sqrt{x-1}+1-4\)
\(=\left(\sqrt{x-1}-1\right)^2-4=\left(\sqrt{x-1}-3\right)\left(\sqrt{x-1}+1\right)\)
b) \(x-2\sqrt{x-6}-5-y^2=\left(x-6\right)-2\sqrt{x-6}+1-y^2\)
\(=\left(\sqrt{x-6}-1\right)^2-y^2=\left(\sqrt{x-6}-1+y\right)\left(\sqrt{x-6}-1-y\right)\)
c) \(x-2\sqrt{x-8}-7-a^2=\left(x-8\right)-2\sqrt{x-8}+1-a^2\)
\(=\left(\sqrt{x-8}-1\right)^2-a^2=\left(\sqrt{x-8}+a-1\right)\left(\sqrt{x-8}-a-1\right)\)
a) \(\left(\sqrt{x-1}-3\right)\left(\sqrt{x-1}+1\right)\)
b) \(\left(\sqrt{x-6}-1-y\right)\left(\sqrt{x-6}-1+y\right)\)
c) \(\left(\sqrt{x-8}-1-a\right)\left(\sqrt{x-8}-1+a\right)\)
a, \(x-\sqrt{x}\)= \(\sqrt{x}.\left(\sqrt{x}-1\right)\)
b, 3x+6\(\sqrt{x}\)= \(\sqrt{x}.\left(3\sqrt{x}+6\right)\)
c, x+2\(\sqrt{x}+1\)= \(\left(\sqrt{x}\right)^2+2\sqrt{x}+1=\left(\sqrt{x}+1\right)^2\)
d, \(3x-5\sqrt{x}+2=3x-3\sqrt{x}-2\sqrt{x}+2\)
=\(3\sqrt{x}.\left(\sqrt{x}-1\right)-2.\left(\sqrt{x}-1\right)\)
=\(\left(3\sqrt{x}-2\right).\left(\sqrt{x}-1\right)\)
\(ab+b\sqrt{a}+\sqrt{a}+1\)
(đk: \(a\ge0\))
\(=b\sqrt{a}\left(\sqrt{a}+1\right)+\sqrt{a}+1=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)
ĐK: \(x,y\ge0\)
\(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}=x\left(\sqrt{x}+\sqrt{y}\right)-y\left(\sqrt{x}+\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(x-y\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)^2\left(\sqrt{x}-\sqrt{y}\right)\)
tui lại
úi sao bạn cũng là quản lý giống mình à, mình trả lời câu hỏi của bạn có được không nhỉ
a) (x -\(\sqrt{2}\))(x+\(\sqrt{2}\))
b) (\(\sqrt{3}x\)-1)(\(\sqrt{3}x\)+1)
c) (\(\sqrt{x}+\sqrt{y}\))(x - \(\sqrt{xy}\)+ y)
d) (2\(\sqrt{x}\)- 3)(4x + 6\(\sqrt{x}\)+ 6)
a) x2 -2 = ( x-\(\sqrt{2}\))(x+\(\sqrt{2}\))
b) 3x2 -1 = ( \(\sqrt{3}\)x -1 ) ( \(\sqrt{3}\)x +1)
c) \(\sqrt{x}\)3 +\(\sqrt{y}\)3= (\(\sqrt{x}\)+\(\sqrt{y}\) )(x-\(\sqrt{xy}\) + y)
d) 8\(\sqrt{x}\)3 -27 = ( 2\(\sqrt{x}\) -3) (4x+ 6\(\sqrt{x}\) +9)\(\)
a/ \(\left(\sqrt{x}-\sqrt{2}\right)\left(\sqrt{x}+\sqrt{2}\right)\)
b/ \(\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1\right)\)
c/ \(\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
d/ \(\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{3}+9\right)\)
a) (x-\(\sqrt{2}\))(x+\(\sqrt{2}\))
b) (\(\sqrt{3}\)x-1)(\(\sqrt{3}\)x+1)
c) (\(\sqrt{x}+\sqrt{y}\))(x-\(\sqrt{xy}\)+y)
d) (2\(\sqrt{x}\)-3)(4x+6\(\sqrt{x}\)+9)
a)\(\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
b) \(\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1\right)\)
c)
d) \(\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a)\(\left(\sqrt{x}-\sqrt{2}\right)\left(\sqrt{x}+\sqrt{2}\right)\)
b) \(\left(\sqrt{3x}-1\right)\left(\sqrt{3x}+1\right)\)
c)\(\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
d)\(\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a,(x-\(\sqrt{2}\))(x+\(\sqrt{2}\))
b,(\(\sqrt{3}\)x-1)(\(\sqrt{3}\)x+1)
c,(\(\sqrt{x}\)+\(\sqrt{y}\))(x-\(\sqrt{x}\)\(\sqrt{y}\)+y)
d,(2\(\sqrt{x}\)-3)(4x+6\(\sqrt{x}\)+9)
a) \(\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)\)
b) \(\left(\sqrt{3}x+1\right)\left(\sqrt{3}x-1\right)\)
c) \(\left(x+y\right)\left(x^2-xy+y^2\right)\)
d) \(\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a. x\(^2\)-2= x\(^2\)- (\(\sqrt{2}\))\(^2\)= (x+\(\sqrt{2}\))(x-\(\sqrt{2}\))
b. 3x\(^2\)-1= (x\(\sqrt{3}\))\(^2\)-1= (x\(\sqrt{3}\)-1)(x\(\sqrt{3}\)+1)
c. \(\sqrt{x^3}+\sqrt{y^3}\)= (x+y)(\(\sqrt{x^2}+\sqrt{xy}+\sqrt{y^2}\))
d.\(8\sqrt{x^3}-27=\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a) x2 - 2=\(\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
b) 3x2 -1=\(\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1\right)\)
c) \(\sqrt{x^3}+\sqrt{y^3}\)=\(\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
d) \(8\sqrt{x^3}-27\)=\(\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a)\(x^2-2=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
b)\(3x^2-1=\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1\right)\)
c)\(\sqrt{x^3}+\sqrt{y^3}=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
d)\(8\sqrt{x^3}-27=\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a) x^2-2=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)x2−2=(x−2)(x+2)
b) 3x^2-1=\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1\right)3x2−1=(3x−1)(3x+1)
c) \sqrt{x^3}+\sqrt{y^3}=\left(\sqrt{x}\right)^3+\left(\sqrt{y}\right)^3=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)x3+y3=(x)3+(y)3=(x+y)(x−xy
a) \(\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
b) \(\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1_{ }\right)\)
c) \(\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
d) \(\left(2\sqrt{x}-3\right)\left(4x+12\sqrt{x}+9\right)\)
a)\(\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
b)\(\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1\right)\)
c)\(\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
d)\(\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a) \(\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)\)
b) \(\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1\right)\)
c) \(\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
d) \(\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a) X^2+2=(x+\(\sqrt{2}\))(x-\(\sqrt{2}\))
a) \(x^2-2=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
b) \(3x^2-1=\left(x\sqrt{3}-1\right)\left(x\sqrt{3}+1\right)\)
c) \(\sqrt{x^3}+\sqrt{y^3}=\left(\sqrt{x}+\sqrt{y}\right)\left[\left(\sqrt{x}\right)^2-\sqrt{xy}+\left(\sqrt{y}\right)^2\right]=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
d)\(8\sqrt{x^3}-27=\left(2\sqrt{x}-3\right)\left[\left(2\sqrt{x}\right)^2+6\sqrt{x}+3^2\right]=\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a) x^2-2
=x^2-√2^2
=(x-√2) (x+√2)
b)3x^2-1
=3x^2-1^2
=(3x-1) (3x+1)
c)√x^3 + √y^3
=(√x-√y) (√x^2-√x√y+√y^2)
d) 8√x^3 -27
=(2√x)^3-3^3
=(2√x-3) ((2√x)^3 +2√x.3+3^2)
a) \(x^2-2\)
\(=x^2-\left(\sqrt{2}\right)^2\)
\(=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
b) \(3x^2-1\)
\(=\left(\sqrt{3x^2}\right)^2-1^2\)
\(=\left(\sqrt{3x^2}-1\right)\left(\sqrt{3x^2}+1\right)\)
\(=\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1\right)\)
c) \(\sqrt{x^3}+\sqrt{y^3}\)
\(=\left(\sqrt{x}\right)^3+\left(\sqrt{y}\right)^3\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
d) \(8\sqrt{x^3}-27\)
\(=\left(2\sqrt{x}\right)^3-3^3\)
\(=\left(2\sqrt{x}-3\right)[\left(2\sqrt{x}\right)^2+2\sqrt{x}\times3+3^2]\)
\(=\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a) x2-2 = (x-\(\sqrt{2}\))(x+\(\sqrt{2}\))
b) 3x2-1 = (\(\sqrt{3}\)x)2-(\(\sqrt{1}\))2 = (\(\sqrt{3}\)x+\(\sqrt{1}\))(\(\sqrt{3}\)x-\(\sqrt{1}\))
c) \(\sqrt{x^3}\)+\(\sqrt{y^3}\) = (\(\sqrt{x}\)+\(\sqrt{y}\))(\(\sqrt{x^2}\)- \(\sqrt{xy}\)+\(\sqrt{y^2}\)) =
d)8\(\sqrt{x^3}\)-27 = (2\(\sqrt{x}\))3-33 = (2\(\sqrt{x}\)-3)
a, \(x^2-2=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
b, \(3x^2-1=\left(\sqrt{3x}-1\right)\left(\sqrt{3x}+1\right)\)
c, \(\sqrt{x^3}+\sqrt{y^3}=\left(\sqrt{x}\right)^3+\left(\sqrt{y}\right)^3=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{x}\sqrt{y}+\sqrt{y}\right)\)
d,\(8\sqrt{x}^3-27=\left(2\sqrt{x}\right)^3-3^3=\left(2\sqrt{x}-3\right)\left(4x+6\sqrt{x}+9\right)\)
a,x2--2=(x --2)(x +2)
b,3x2 --1=(√3x --1)(√3X+1)
C,√x3+√y3=(√x)3+(√y)3=(√x+√y)(x-\(\sqrt{ }\)xy+y)
D,8√x3--27=(2√x)3--33=(2√x-3)(4x+6√x+9)