Question

Bài 1: Rút gọn:

a) (x-3)(x+3)-(2x-3)

b) (a+b)²+(a-b)²-2(b-a)(b+a)

Bài 2: Chứng minh rằng:

a) x²-x+1>0 với mọi x

b) x-x²-2<0 với mọi x

Các bạn giúp mình với nha! ^-^

Answer 1

\(\left(x-3\right)\left(x+3\right)-\left(2x-3\right)\)

\(=x^2-9-2x+3\)

\(=x^2-2x-6\)

\(\left(a+b\right)^2+\left(a-b\right)^2-2\left(b-a\right)\left(b+a\right)\)

\(=a^2+2ab+b^2+a^2-2ab+b^2-2\left(b^2-a^2\right)\)

\(=2a^2+2b^2-2a^2-2b^2\)

\(=0\)

2) \(x^2-x+1=x^2-x+\dfrac{1}{4}+\dfrac{3}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0\left(đpcm\right)\)

\(x-x^2-2=-x^2+x-2=-\left(x^2-x+2\right)=-\left(x^2-x+\dfrac{1}{4}+\dfrac{7}{4}\right)=-\left(x^2-x+\dfrac{1}{4}\right)-\dfrac{7}{4}=-\left(x-\dfrac{1}{2}\right)^2-\dfrac{7}{4}< 0\left(đpcm\right)\)

Answer 2

Answer 3