Question

Bài 1 : cm

a) \(^{x^2}\)-2xy +\(^{y^2}\)+ 1 > 0   \(\forall\)xy

b) x-\(x^2\)-1<0 \(\forall\)x

c) 9\(x^2\)+12x+10 >0

d) 3\(^{x^2}\)-x+ 1>0

Giúp mk ,mk cần gấp

ai nhanh mk tick cho !!

Answer 1

a)\(x^2-2xy+y^2+1=\left(x+y\right)^2+1\ge1>0\)

b)\(x-x^2-1=-\left(x^2-x+\frac{1}{4}\right)^2-\frac{3}{4}\le-\frac{3}{4}< 0\)

c)\(9x^2+12x+10=\left(9x^2+12x+4\right)+6=\left(3x+2\right)^2+6\ge6>0\)

d)\(3x^2-x+1=2x^2+\left(x^2-x+\frac{1}{4}\right)+\frac{3}{4}=2x^2+\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}>0`\)