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If x = \(\frac{\sqrt{3}+{\sqrt2}}{\sqrt{3}-{\sqrt2}}\) and y = \(\frac{\sqrt{3}-{\sqrt2}}{\sqrt{3}+{\sqrt2}}\) then the value of x + y 

x = (√3+√2)/(√3-√2) and y = (√3-√2)/(√3+√2) 

A) 5 

B) 5 + 2√6 

C) 10 

D) 5 – 2√6

2 Answers

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by (57.0k points)
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Best answer

Correct option is (C) 10

x+y \(=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}\)

\(=\frac{(\sqrt{3}+\sqrt{2})^2+(\sqrt{3}-\sqrt{2})^2}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}\)

\(=\frac{(3+2+2\sqrt6)+(3+2-2\sqrt6)}{3-2}\)

\(=\frac{5+5}1=10\)

+1 vote
by (38.9k points)

Correct option is  C) 10

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