Question

$sqrt{x sqrt[5]{x} } - sqrt[5]{x sqrt{x} } = 56$

Answer 1

$mathtt{sqrt{xsqrt[5]{x}}-sqrt[5]{xsqrt{x}}=56;~x^{(1+frac{1}{5})frac{1}{2}}-x^{(1+frac{1}{2})frac{1}{5}}=56;~x^{frac{3}{10}}-x^{frac{3}{5}}+56=0;}\mathtt{(x^{frac{3}{10}})^2-x^{frac{3}{10}}-56=0;~(x^{frac{3}{10}}+7)(x^{frac{3}{10}}-8)=0~to~x^{frac{3}{10}}-8=0;~x^{frac{3}{10}}=8;}\mathtt{x=8^{frac{10}{3}}=(2^3)^{frac{10}{3}}=2^{10}=1024}$