Question

[Yến Hoàng]

Mấy bạn giải giúp mình câu 2,4b,5v nha, ths nhìu !!!!

Answer 1

[Hồng Trinh]

4b. ta có : \(\frac{\left(x_1-1\right)\left(x_2-1\right)-1}{x_1+x_2-2}-\frac{x_1+x_2}{4}\)\(=\frac{x_1x_2-x_1-x_2+1-1}{x_1+x_2-2}-\frac{x_1+x_2}{4}=\frac{x_1x_2-\left(x_1+x_2\right)}{\left(x_1+x_2\right)-2}-\frac{x_1+x_2}{4}\)

Ta có : \(x_1x_2=\frac{c}{a}=m^2+2\) ; \(x_1+x_2=\frac{-b}{a}=2\left(m+1\right)\)

Nên: \(\frac{m^2+2-2\left(m+1\right)}{2\left(m+1\right)-2}-\frac{2\left(m+1\right)}{4}=\frac{m^2+2-2m-2}{2m}-\frac{m+1}{2}=\frac{m^2-2m-m^2-m}{2m}=\frac{-3m}{2m}=\frac{-3}{2}\) \(< 0\) với mọi m .(đpcm)