Question

x phần 4 = y phần 7 và y mũ 2 - x mũ 2 = 66

 

Answer 1

Đặt \(\dfrac{x}{4}=\dfrac{y}{7}=k\Rightarrow x=4k.y=7k\)

Ta có:\(y^2-x^2=66\\ \Rightarrow\left(7k\right)^2-\left(4k\right)^2=66\\ \Rightarrow49k^2-16k^2=66\\ \Rightarrow33k^2=66\\ \Rightarrow k^2=2\\ \Rightarrow\left[{}\begin{matrix}k=\sqrt{2}\\k=-\sqrt{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\sqrt{2};y=7\sqrt{2}\\x=-4\sqrt{2};y=-7\sqrt{2}\end{matrix}\right.\)