Cho 3 số thực x,y,z thỏa mãn \(x+y=\left(\sqrt{x}+\sqrt{y}-\sqrt{z}\right)^2\)

Chứng minh: \(\dfrac{x+\left(\sqrt{x}-\sqrt{z}\right)^2}{y+\left(\sqrt{y}-\sqrt{z}\right)^2}=\dfrac{\sqrt{x}-\sqrt{z}}{\sqrt{y}-\sqrt{z}}\)

\(103^2=\left(100+3\right)^2=100^2+2.3.100+3^2=10000+600+9=10609\)

\(52.48=\left(50+2\right)\left(50-2\right)=50^2-2^2=2500-4=2496\)

\(75^2-50.75+25^2=75^2-25.75-25.75+25^2=75\left(75-25\right)-25\left(75-25\right)=\left(75-25\right)=50^2=2500\)