Question

a) Tìm GTLN A= \(\frac{2x^2+9}{x^2+4}\)

b) Tìm GTNN B=\(\frac{3x^2-8x+13}{x^2+5}\)

Giúp mình càng sớm càng tốt nha :))

Answer 1

a) \(A=\frac{2x^2+9}{x^2+4}=\frac{\left(2x^2+8\right)+1}{x^2+4}=\frac{2\left(x^2+4\right)+1}{x^2+4}=2+\frac{1}{x^2+4}\)

Ta thấy \(x^2\ge0\forall x\)

=> \(x^2+4\ge4\forall x\)

=> \(\frac{1}{x^2+4}\le\frac{1}{4}\forall x\)

=> \(A\le\frac{1}{4}+2=\frac{9}{4}\)

\(MaxA=\frac{9}{4}\Leftrightarrow x=0\)