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\(x.\left(x-\frac{1}{2}\right)=1+x.x\)
\(x^2-\frac{1}{2}x=1+x^2\)
\(\frac{-1}{2}x=1+x^2-x^2\)
\(\frac{-1}{2}x=1\)
\(\Leftrightarrow x=1:\frac{-1}{2}=-2\)
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a) \(x\times x+372=472\)
\(x^2=100\)
\(x=10;-10\)
b) \(69,5-x\times x=20,5\)
\(69,5-x^2=20,5\)
\(-x^2+69,5=20,5\)
\(-x^2=-49\)
\(x^2=49\)
\(x=-7;7\)
c) \(x\times x-\dfrac{1}{6}=\dfrac{5}{18}\)
\(x^2=\dfrac{4}{9}\)
\(x=\dfrac{2}{3};-\dfrac{2}{3}\)
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x.x-2 chia het cho x-1
\(\Rightarrow\)x.x-x+x-2 chia het cho x-1
\(\Rightarrow\)x.(x-1)+x-1-1 chia het cho x-1
\(\Rightarrow\)1 chia het cho x-1
\(\Rightarrow\)x-1\(\in\){1;-1}
Voi x-1=1\(\Rightarrow\)x=2
Voi x-1=-1\(\Rightarrow\)x=0
Vay x\(\in\){2;0}
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\(1+x.x=2+4+6+....+250.\)
\(1+2.x=\left\{\left(250+2\right).\left(\left\{250-2\right\}:2+1\right):2\right\}\)
\(1+2.x=15750\)
\(2.x=15750-1\)
\(2.x=15749\)
\(x=15749:2=7874,5\)
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x^3-x-2x^2-2