Question

cho P=\(\dfrac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+3}+\dfrac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\dfrac{3\sqrt{z}}{\sqrt{zx}+3\sqrt{z}+3}\) với x,y,z là các số không âm thỏa mãn: xyz=9. Tính \(\sqrt{10P-1}\)

Answer 1

P = 1

Sqrt(10P - 1) = sqrt(10.1-1)=3

Answer 2

\(P=\dfrac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+3}+\dfrac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\dfrac{3\sqrt{z}}{\sqrt{zx}+3\sqrt{x}+3}\)

\(=\dfrac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+\sqrt{xyz}}+\dfrac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\dfrac{\sqrt{xyz}\sqrt{z}}{\sqrt{zx}+\sqrt{xyz}\sqrt{z}+\sqrt{xyz}}\)

\(=\dfrac{1}{\sqrt{y}+1+\sqrt{yz}}+\dfrac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\dfrac{\sqrt{yz}}{1+\sqrt{yz}+\sqrt{y}}\)

\(=\dfrac{1+\sqrt{y}+\sqrt{yz}}{1+\sqrt{y}+\sqrt{yz}}=1\)

\(\Rightarrow\sqrt{10P-1}=\sqrt{10.1-1}=\sqrt{9}=3\)