Question

Solve the equation:

$(x-\sqrt{3}{)}^4-5(x-\sqrt{3}{)}^2+4=0$

Answer 1

$(x-\sqrt{3}{)}^4-5(x-\sqrt{3}{)}^2+4=0$

Let $(x-\sqrt{3}{)}^2$ be $t$, $t\ge 0$

$t^2-5t+4=0$

$(t-4)(t-1)=0$

$t=1,4$

When $t=1$

$(x-\sqrt{3}{)}^2=1$

$x-\sqrt{3}=\pm 1$

$x=\sqrt{3}\pm 1$

When $t=4$

$(x-\sqrt{3}{)}^2=4$

$(x-\sqrt{3})=\pm 2$

$x=\sqrt{3}\pm 2$