Question

(√125 - √28)-(√63 - √20)=X√5 - 5√X

Answer 1

 

$\displaystyle\\\Big(\sqrt{125}-\sqrt{28}\Big)-\Big(\sqrt{63}-\sqrt{20}\Big)=x\sqrt{5}-5\sqrt{x}\\\\\\\Big(\sqrt{25\cdot5}-\sqrt{4\cdot7}\Big)-\Big(\sqrt{9\cdot7}-\sqrt{4\cdot5}\Big)=x\sqrt{5}-5\sqrt{x}\\\\\\\Big(5\sqrt{5}-2\sqrt{7}\Big)-\Big(3\sqrt{7}-2\sqrt{5}\Big)=x\sqrt{5}-5\sqrt{x}\\\\\\5\sqrt{5}-2\sqrt{7}-3\sqrt{7}+2\sqrt{5}=x\sqrt{5}-5\sqrt{x}\\\\\\5\sqrt{5}+2\sqrt{5}-2\sqrt{7}-3\sqrt{7}=x\sqrt{5}-5\sqrt{x}$

$\displaystyle\\7\sqrt{5}-5\sqrt{7}=x\sqrt{5}-5\sqrt{x}\\\\\\7\sqrt{5}=x\sqrt{5}~~~\implies~\boxed{x_1=7}\\\\\\-5\sqrt{7}=-5\sqrt{x}~~~\implies~\boxed{x_2=7}$