Bài 1 .Cho x = a+b/c = b+c/a = c+a/b ( a,b,c khác 0)
Tính A=( x2 + x+1)100
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2: \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0\)
=>\(\frac{xy+yz+xz}{xyz}=0\)
=>xy+yz+xz=0
=>xy=-xz-yz; yz=-xy-xz; xz=-xy-yz
\(x^2+2yz=x^2+yz+yz\)
\(=x^2+yz-xy-xz=x\left(x-y\right)-z\left(x-y\right)=\left(x-y\right)\left(x-z\right)\)
\(y^2+2xz=y^2+xz+xz\)
\(=y^2+xz-xy-yz=y^2-xy+xz-yz\)
=y(y-x)+z(x-y)
=z(x-y)-y(x-y)=(x-y)(z-y)
\(z^2+2xy\)
\(=z^2+xy+xy\)
\(=z^2+xy-yz-xz\)
\(=z^2-xz+xy-yz=z\left(z-x\right)+y\left(x-z\right)=\left(x-z\right)\left(y-z\right)\)
\(A=\frac{yz}{x^2+2yz}+\frac{xz}{y^2+2xz}+\frac{xy}{z^2+2xy}\)
\(=\frac{yz}{\left(x-y\right)\left(x-z\right)}+\frac{xz}{\left(x-y\right)\left(z-y\right)}+\frac{xy}{\left(x-z\right)\left(y-z\right)}\)
\(=\frac{yz\left(y-z\right)-xz\left(x-z\right)+xy\left(x-y\right)}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}=\frac{y^2z-yz^2-x^2z+xz^2+x^2y-xy^2}{\left(x-y\right)\cdot\left(x-z\right)\left(y-z\right)}\)
\(=\frac{z\left(y^2-x^2\right)+z^2\left(x-y\right)+xy\left(x-y\right)}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}=\frac{\left(x-y\right)\left\lbrack-z\left(x+y\right)+z^2+xy\right\rbrack}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}\)
\(=\frac{-xz-yz+z^2+xy}{\left(x-z\right)\left(y-z\right)}=\frac{z^2-yz-xz+xy}{\left(x-z\right)\left(y-z\right)}=\frac{z\left(z-y\right)-x\left(z-y\right)}{\left(x-z\right)\left(y-z\right)}=\frac{\left(z-x\right)\left(z-y\right)}{\left(z-x\right)\left(z-y\right)}\)
=1
Bài 4: B
Bài 5:
a: {3;5};{3;7};{5;7};{3;5;7};{3};{5};{7};\(\varnothing\)
a x b = b x a
( a x b ) x c = a x ( b x c )
a x 1 = 1 x a = a
a x ( b + c ) = a x b + a xc
a : 1 = a
Câu ...a = a sai đề
a : a = 1
0 : a = 0
TK mk nha o0o công chúa sinh đôi o0o
Tk mk nha các bn
Ai tk mk.mk tk lại
Bài 1:
a x b = b x a
(a x b) x c = a x (b x c)
a x 1 = 1 x a = a
a x (b + c) = a x b + a x c
a : 1 = a
... : a = a là sai. Nên sửa là: ... : a = 1
a : a = 1
0 : a = 0
\(x=\frac{a+b}{c}=\frac{b+c}{a}=\frac{c+a}{b}\)
Cộng 1 vào mỗi tỉ số ta được :
\(x+1=\frac{a+b}{c}+1=\frac{b+c}{a}+1=\frac{c+a}{b}+1\)
\(x+1=\frac{a+b+c}{c}=\frac{a+b+c}{a}=\frac{a+b+c}{b}\)
Xét a + b + c = 0
\(\Rightarrow\)a + b = -c ; b + c = -a ; a + c = -b
\(\Rightarrow\)\(x=\frac{-c}{c}=\frac{-a}{a}=\frac{-b}{b}=-1\)
\(\Rightarrow\)( x2 + x + 1 )100 = [ ( -1 )2 + ( -1 ) + 1 ]100 = 1100 = 1
Xét a + b + c \(\ne\)0 thì a = b = c
\(\Rightarrow x=\frac{a+b}{c}=\frac{b+c}{a}=\frac{c+a}{b}=2\)
\(\Rightarrow\)( x2 + x + 1 )100 = ( 22 + 2 + 1 )100 = 7100
thanks nhìu