Question

prove that prove
$\frac{1}{2 + \sqrt{3} } + \frac{2}{ \sqrt{5 - \sqrt{3} } } + \frac{1}{2 - \sqrt{5} } = 0$
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Answer 1

Answer:

Let , 1/2 - √5 be a rational number

Then,

1/2-√5 = p/q

2-√5 = q/p

√5 = 2-q/p

√5 = 2 - p/q

√5 = 2q/p

2p/q is a rational number, then √5 should be rational too.

.

But, this contradicts the fact that √5 is an irrational number, so our supposition is totally wrong and 1/2-√5 is an irrational number.

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Hope it helps...!!!