Câu 10:
a) Ta có: \(A=-x^2+4x+3\)
\(=-\left(x^2-4x-3\right)\)
\(=-\left(x^2-4x+4-7\right)\)
\(=-\left(x-2\right)^2+7\le7\forall x\)
Dấu '=' xảy ra khi x=2
b) Ta có: \(B=-x^2+x\)
\(=-\left(x^2-x+\dfrac{1}{4}-\dfrac{1}{4}\right)\)
\(=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}\le\dfrac{1}{4}\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{1}{2}\)
c) Ta có: \(C=-2x^2+2x-5\)
\(=-2\left(x^2-x+\dfrac{5}{2}\right)\)
\(=-2\left(x^2-x+\dfrac{1}{4}+\dfrac{9}{4}\right)\)
\(=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{2}\le-\dfrac{9}{2}\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{1}{2}\)
Câu 11:
a) Ta có: \(\left(a-b\right)^3\)
\(=\left[-1\cdot\left(b-a\right)\right]^3\)
\(=\left(-1\right)^3\cdot\left(b-a\right)^3\)
\(=-\left(b-a\right)^3\)
b) Ta có: \(\left(-a-b\right)^2\)
\(=\left[-\left(a+b\right)\right]^2\)
\(=\left(-1\right)^2\cdot\left(a+b\right)^2\)
\(=\left(a+b\right)^2\)
