Question

Answer 1

a: \(P=\dfrac{x-4+5}{\sqrt{x}+2}=\sqrt{x}-2+\dfrac{5}{\sqrt{x}+2}\)

=>\(P=\sqrt{x}+2+\dfrac{5}{\sqrt{x}+2}-4>=2\cdot\sqrt{\left(\sqrt{x}+2\right)\cdot\dfrac{5}{\sqrt{x}+2}}-4=2\sqrt{5}-4\)

Dấu = xảy ra khi (căn x+2)^2=5

=>căn x+2=căn 5

=>căn x=căn 5-2

=>x=9-4căn 5
b: \(Q=\dfrac{x-9+14}{\sqrt{x}+3}=\sqrt{x}-3+\dfrac{14}{\sqrt{x}+3}\)

=>\(Q=\sqrt{x}+3+\dfrac{14}{\sqrt{x}+3}-6\)

=>\(Q>=2\sqrt{14}-6\)

Dấu = xảy ra khi (căn x+3)^2=14

=>\(\sqrt{x}+3=\sqrt{14}\)

=>\(\sqrt{x}=\sqrt{14}-3\)

=>\(x=23-6\sqrt{14}\)