If (√(3+(√2))) = (√((a+(√b))/c)) + (√((a−(√b))/c)) then a+bc = ?


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Question Number 136340 by liberty last updated on 21/Mar/21

$I f \sqrt{3 + \sqrt{2}} = \sqrt{\frac{a + \sqrt{b}}{c}} + \sqrt{\frac{a - \sqrt{b}}{c}}$ $t h e n a + b c = ?$
	Answered by Ñï= last updated on 21/Mar/21

	$\sqrt{3 + \sqrt{2}} = \sqrt{x} + \sqrt{y}$ $3 + \sqrt{2} = x + y + 2 \sqrt{x y}$ $\Rightarrow {\begin{cases} 3 = x + y \\ \sqrt{2} = 2 \sqrt{x y} \end{cases}$ $\Rightarrow x = \frac{3 + \sqrt{7}}{2} y = \frac{3 - \sqrt{7}}{2}$ $\Rightarrow a = 3 b = 7 c = 2$ $a + b c = 17$
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