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If the sum of the square roots of two integers is

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Re: If the sum of the square roots of two integers is  [#permalink]

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New post 25 Oct 2018, 00:48
1
how do we know that
x+y=9
and
2 square root of xy= 6 square root of 2
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Re: If the sum of the square roots of two integers is  [#permalink]

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New post 25 Oct 2018, 01:08
Bunuel wrote:
If the sum of the square roots of two integers is \(\sqrt{9+6\sqrt{2}}\), what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52


Let the two integers be a and b.

\(\sqrt{a} + \sqrt{b} = \sqrt{9+6\sqrt{2}}\)

Squaring both sides, we get

\(a + b + 2\sqrt{ab} = 9 + 6\sqrt{2}\)

Since a and b are integers, so \(2\sqrt{ab} = 6\sqrt{2}\)

\(\sqrt{ab} = 3*\sqrt{2} = \sqrt{3*3*2}\)

So values of a and b such that ab = 3*3*2 and sum is 9 is 6 and 3.

\(a^2 + b^2 = 6^2 + 3^2 = 45\)

Answer (C)
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Re: If the sum of the square roots of two integers is   [#permalink] 25 Oct 2018, 01:08

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