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if [sqrt(a) + sqrt(b)]/ [sqrt(a) – sqrt(b)] + [sqrt(a) – sqrt(b)]/ [sqrt(a) + sqrt(b)] = a – b, then prove that a – b = sqrt (2)

if [sqrt(a) + sqrt(b)]/ [sqrt(a) – sqrt(b)] + [sqrt(a) – sqrt(b)]/ [sqrt(a) + sqrt(b)] = a – b, then prove that a – b = sqrt (2)

Grade:12th pass

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question below
Given\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}+\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}=a-b
Taking lcm we get
{(\sqrt{a}+\sqrt{b})^{2}}+{(\sqrt{a}-\sqrt{b})^{2^{}}}=(a-b)^{2}
On expanding we get
(a-b)2=2(a+b)
so you get (a-b)=\pm \sqrt{2}(a+b)
I think there is some error in the question

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