Question

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Answer 1

Answer:

Step-by-step explanation

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Answer 2

Answer:

Step-by-step explanation:

The given equation is:

$(a-b)^{2}v^{2}+(a-b)v-(a+b)=\sqrt{a}+\sqrt{b}+2\sqrt{a}\sqrt{b}$

If v=$\frac{1}{\sqrt{a}-\sqrt{b}}$, then rationalising this function,

v=$\frac{\sqrt{a}+\sqrt{b}}{a-b}$

Now, LHS of the above equation,

=$(a-b)^{2}{\times}(\frac{\sqrt{a}+\sqrt{b}}{a-b})^{2}+(a-b){\times}(\frac{\sqrt{a}+\sqrt{b}}{a-b})-a-b$

=$a+b+2\sqrt{a}\sqrt{b}+\sqrt{a}+\sqrt{b}-a-b$

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

=RHS

Henec proved.