Question

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

Answer 1

ОДЗ: x≥0;

$sqrt{xsqrt[5]{x}}-sqrt[5]{xsqrt{x}}=56;\sqrt{x^{1,2}}-sqrt[5]{x^{1,5}}=56;\x^{0,3*2}-x^{0,3}-56=0; t=x^{0,3}; tgeq 0;$

t²-t-56=0;

D=1+4*56=225;

t₁=(1-15)/2=-7; ∅ t≥0;

t₂=(1+15)/2=8;

$t=x^{0,3}=sqrt[10]{x^3}=sqrt[10]{x^3}=8=2^3; x=2^10;x^{0,6}-x^{0,3}-56=0;\2^6-2^3=56;\56=56;$

x=2¹⁰=1024;