Question

Giúp ạ huhu

Answer 1

a: \(A=x^2-8x+16+4=\left(x-4\right)^2+4>0\)

b: \(B=4x^2-12x+9+2=\left(2x-3\right)^2+2>0\)

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

d: \(D=x^2-2x+1+y^2+4y+4+1\)

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

Answer 2

\(a)\\ A=x^2-8x+20\\ =x^2-8x+16+4\\ =\left(x-4\right)^2+4>0\\ b)\\B= 4x^2-12x+11\\ =\left(4x^2-2\cdot2x\cdot3+9\right)+2\\ =\left(2x-3\right)^2+2>0\\ c)\\ C=x^2-x+1\\ =x^2-2\cdot x\cdot\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{3}{4}\\ =\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0\\ d)\\ D=x^2-2x+y^2+4y+6\\ =x^2-2x+1+y^2+4y+4+1\\ =\left(x-1\right)^2+\left(y+2\right)^2+1>0\)