Question

GTNN
A = 4x\(^{^{ }2}\) - 12x + 10
B = 3y\(^2\) + 6y + 5

Answer 1

a) \(A=4x^2-12x+10\)

\(A=4x^2-12x+9+1\)

\(A=\left(2x-3\right)^2+1\)

Vì \(\left(2x+3\right)^2\ge0\forall x\)

\(\Rightarrow\left(2x+3\right)^2+1\ge1\forall x\)

Dấu "=" xảy ra \(\Leftrightarrow2x+3=0\Leftrightarrow x=-1,5\)

Vậy \(MIN_A=1\Leftrightarrow x=-1,5\)

b) \(B=3y^2+6y+5\)

\(B=3\left(y^2+2y+\dfrac{5}{3}\right)\)

\(B=3\left(y^2+2y+1+\dfrac{2}{3}\right)\)

\(B=3\left(y+1\right)^2+2\)

Vì \(3\left(y+1\right)^2\ge0\forall x\)

\(\Rightarrow3\left(y+1\right)^2+2\ge2\forall x\)

Dấu "=" xảy ra \(\Leftrightarrow y+1=0\Leftrightarrow y=-1\)

Vậy \(MIN_B=2\Leftrightarrow x=-1\)