Question

C/m bt luôn dương với mọi x:

a.x^2-8x+19

b.3x^2-6x+5

c.x^2+y^2-8x+4y+27

Answer 1

a ) \(x^2-8x+19\)

\(=x^2-2x.4+16+3\)

\(=\left(x-4\right)^2+3\ge3\forall x\left(đpcm\right)\)

b ) \(3x^2-6x+5\)

\(=3\left(x^2-2x+\dfrac{5}{3}\right)\)

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

\(=3\left[\left(x-1\right)^2+\dfrac{2}{3}\right]\)

\(=3\left(x-1\right)^2+2\ge2\forall x\left(đpcm\right)\)

c ) \(x^2+y^2-8x+4y+27\)

\(=\left(x^2-8x+16\right)+\left(y^2+4y+4\right)+7\)

\(=\left(x-4\right)^2+\left(y+2\right)^2+7\ge7\forall x\left(đpcm\right)\)

:D