Question

Решить для х 1-x=(1-(4x^2-7x^4)^1/2)^1/2

Answer 1

$1-x=(1-\sqrt{4x^2-7x^4} ) ^{\frac{1}{2} }$

$1-x=\sqrt{1-\sqrt{4x^2-7x^4}}$

$1-x=\sqrt{1-x\sqrt{4-7x^2}}$

$1-x\sqrt{4-7x^2}=1-2x+x^2$

$-x\sqrt{4-7x^2}=-2x+x^2$

$x^2*(4-7x^2)=x^4-4x^3+4x^2$

$4x^2-7x^4=x^4-4x^3+4x^2$

$-7x^4=x^4-4x^3$

$-7x^4-x^4+4x^3=0$

$-8x^4+4x^3=0$

$-4x^3*(2x-1)=0$

$x^3*(2x-1)=0$

$\left \{ {{x^3=0} \atop {x=\frac{1}{2} }} \right.$

$\left \{ {{x=0} \atop {x=0,5 }} \right.$