Question

Реши уравнение
$x + \sqrt{x} = 25.$
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Answer 1

$x+\sqrt x=25,~~t=\sqrt x,~x\geq 0,~t\geq 0\\t^2+t-25=0\\t=\dfrac{-1\pm\sqrt{1^2+4\cdot25}}{2}\\t=\dfrac{-1\pm\sqrt{101}}2\\t=\dfrac{-1+\sqrt{101}}2,~t\geq 0\\\sqrt x=\dfrac{-1+\sqrt{101}}2\\x=\bigg(\dfrac{-1+\sqrt{101}}2\bigg)^2\\x=\dfrac{1-2\sqrt{101}+101}{4}\\x=\dfrac{102-2\sqrt{101}}4 \\\\\\x=\dfrac{\fbox{102}-2\sqrt{\fbox{101}}}{\fbox{4}}$