If-3-2-a-b-c-a-b-c-then-a-bc-

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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