Question

If (√(5) + √(6)) ^ 2 = a + b √(30) then a and b respectively are (A) 12 and 2 (B) √(5) and √(6) (C) 11 and 2 (D) 10 and 2√(30)​

Answer 1

Step-by-step explanation:

$(\sqrt{5} +\sqrt{6} )^{2} = (\sqrt{5} )^{2} +2(\sqrt{5} )(\sqrt{6} )+(\sqrt{6} )^{2}$

$=5+2\sqrt{30} +6\\=11+2\sqrt{30}$

$11+2\sqrt{30} =a+b\sqrt{30}$

∴ a = 11 and b = 2

Hence , (C) 11 and 2 is the correct option.

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