Question

Evaluate :{√(5+2√6)} +{√(8-2√15)}

Answer 1

$let\ \sqrt{5+2\sqrt6}=\sqrt{a}+\sqrt{b}\\\\squaring:\ 5+2\sqrt6=a+b+2\sqrt{ab}\\\\equate\ rational\ and\ irrational\ parts\\\\a+b=5,\ ab=6,\ easy\ to\ know:a=3,\ b=2,\ or\ a=2,b=3\\\\let\ \sqrt{8-2\sqrt{15}}=\sqrt{c}-\sqrt{d},\ minus\ as\ there\ is\ - inside\ square\ root.\\\\squaring\ 8-2\sqrt{15}=c+d-2\sqrt{cd}\\\\ \implies\ c+d=8,\ cd=15\\\\Easy\ to\ know,\ c=5, d=3\ or\ c=3,\ d=5\\\\but\ we\ take\ positive\ square\ root.\\\\Answer=\sqrt{2}+\sqrt{3}+\sqrt{5}-\sqrt{3}=\sqrt{2}+\sqrt{5}$

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We can also find the values of  a, b  or c, d  by solving quadratic equations.

c + d = 8   and  c d = 15   =>  d = 15/c
=>  c + 15/c = 8
=>  c² - 8 c + 15 = 0
=>   c² - 5 c - 3 c + 15 = 0
=>   (c - 5) c - 3 ( c - 5) = 0
=>   (c - 5) ( c - 3) = 0          => c = 5 or 3
=>  d = 3 or 5

Answer 2

Answer:

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THE ANSWER ISSSSSSSSS

I DON'TTTTTT KNOWWWWW!! I AM SORRY BRO

Step-by-step explanation: