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Question

Solve the equation: 
$$(x \, - \, \sqrt{3})^4 \, - \, 5 \, (x \, - \, \sqrt{3} )^2 \, + \, 4 \, = \, 0$$


Solution

$$(x-\sqrt{3})^4 -5(x-\sqrt3)^2 +4=0$$
Let $$(x-\sqrt3)^2$$ be $$t$$, $$t\geq 0$$
$$t^2-5t+4=0$$
$$(t-4)(t-1)=0$$
$$t=1,4$$
When $$t=1$$
$$(x-\sqrt3)^2=1$$
$$x-\sqrt3 =\pm 1$$
$$x=\sqrt3 \pm 1$$
When $$t=4$$
$$(x-\sqrt{3})^2 =4$$
$$(x-\sqrt{3})=\pm 2$$
$$x=\sqrt{3} \pm 2$$

Mathematics

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