Tính nhanh 410 . 510 - (205 - 2)(205 + 2)
x4 - 13x3 + 13x2 - 13x + 112 tại x = 12
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a: Ta có: x=31
nên x-1=30
Ta có: \(A=x^3-30x^2-31x+1\)
\(=x^3-x^2\left(x-1\right)-x^2+1\)
\(=x^3-x^3+x^2-x^2+1\)
=1
c: Ta có: x=16
nên x+1=17
Ta có: \(C=x^4-17x^3+17x^2-17x+20\)
\(=x^4-x^3\left(x+1\right)+x^2\left(x+1\right)-x\left(x+1\right)+20\)
\(=x^4-x^4-x^3+x^3+x^2-x^2-x+20\)
\(=20-x=4\)
d: Ta có: x=12
nên x+1=13
Ta có: \(D=x^{10}-13x^9+13x^8-13x^7+...+13x^2-13x+10\)
\(=x^{10}-x^9\left(x+1\right)+x^8\left(x+1\right)-x^7\left(x+1\right)+...+x^2\left(x+1\right)-x\left(x+1\right)+10\)
\(=10-x\)
=-2
d: Ta có: x=12
nên x+1=13
Ta có: \(D=x^{10}-13x^9+13x^8-13x^7+...+13x^2-13x+10\)
\(=x^{10}-x^9\left(x+1\right)+x^8\left(x+1\right)-x^7\left(x+1\right)+...+x^2\left(x+1\right)-x\left(x+1\right)+10\)
\(=x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...+x^3+x^2-x^2-x+1+9\)
\(=-x+10=-2\)
Ta có: \(\left(0,125\right)^3\cdot8^3+\left(\frac34-\frac56\right)^2-\frac{50^3}{125}+20^5\cdot\frac{5^{10}}{100^5}\)
\(=\left(0,125\cdot8\right)^3+\left(\frac{9}{12}-\frac{10}{12}\right)^2-\frac{\left(5^2\cdot2\right)^3}{5^3}+\frac{5^5\cdot2^{10}\cdot5^{10}}{\left(2^2\cdot5^2\right)^5}\)
\(=1+\left(-\frac{1}{12}\right)^2-\frac{5^6\cdot2^3}{5^3}+5^5=1+\frac{1}{144}-5^3\cdot2^3+5^5\)
\(=\frac{145}{144}+5^3\left(5^2-2^3\right)=\frac{145}{144}+125\cdot17=\frac{306145}{144}\)
Ta có: \(\left(0,125\right)^3\cdot8^3+\left(\frac34-\frac56\right)^2-\frac{50^3}{125}+20^5\cdot\frac{5^{10}}{100^5}\)
\(=\left(0,125\cdot8\right)^3+\left(\frac{9}{12}-\frac{10}{12}\right)^2-\frac{\left(5^2\cdot2\right)^3}{5^3}+\frac{5^5\cdot2^{10}\cdot5^{10}}{\left(2^2\cdot5^2\right)^5}\)
\(=1+\left(-\frac{1}{12}\right)^2-\frac{5^6\cdot2^3}{5^3}+5^5=1+\frac{1}{144}-5^3\cdot2^3+5^5\)
\(=\frac{145}{144}+5^3\left(5^2-2^3\right)=\frac{145}{144}+125\cdot17=\frac{306145}{144}\)
Ta có: \(\left(0,125\right)^3\cdot8^3+\left(\frac34-\frac56\right)^2-\frac{50^3}{125}+20^5\cdot\frac{5^{10}}{100^5}\)
\(=\left(0,125\cdot8\right)^3+\left(\frac{9}{12}-\frac{10}{12}\right)^2-\frac{\left(5^2\cdot2\right)^3}{5^3}+\frac{5^5\cdot2^{10}\cdot5^{10}}{\left(2^2\cdot5^2\right)^5}\)
\(=1+\left(-\frac{1}{12}\right)^2-\frac{5^6\cdot2^3}{5^3}+5^5=1+\frac{1}{144}-5^3\cdot2^3+5^5\)
\(=\frac{145}{144}+5^3\left(5^2-2^3\right)=\frac{145}{144}+125\cdot17=\frac{306145}{144}\)
Bài 2:
a: =>x-45=-20
hay x=25
b: =>35+30-5x=-12+112
=>65-5x=100
=>5x=-35
hay x=-7
c: =>x-124=1000
hay x=1124
d: \(\Leftrightarrow46-\left(3x-2\right)^3=-18\)
\(\Leftrightarrow\left(3x-2\right)^3=64\)
=>3x-2=4
hay x=2
Bài 2:
a: =>x-45=-20
hay x=25
b: =>35+30-5x=-12+112=100
=>65-5x=100
=>5x=-35
hay x=-7
c: =>x-124=1000
hay x=1124
d: \(\Leftrightarrow46-\left(3x-2\right)^3=-18\)
\(\Leftrightarrow\left(3x-2\right)^3=64\)
=>3x-2=4
hay x=2
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