Question

prove that 1/2+root3+2/root5-root3+1/2-root5=0​

Answer 1

Given, 1/(2 + √3) + 2/(√5 - √3) + 1/(2 - √5)

After rationalizing each term, we get

= [{1*(2 - √3)}/{(2 + √3)*(2 - √3)}] + [{2*(√5 + √3)}/{(√5 - √3)*(√5 + √3)}] + [{1*(2 + √5)}/{(2 + √5)*(2 - √5)}]

= (2 - √3)/(4 - 3) + {2*(√5 + √3)}/(5 - 3) + (2 + √5)/(4 - 5)

= (2 - √3) + {2*(√5 + √3)}/2 + (2 + √5)/(-1)

= (2 - √3) + (√5 + √3) - (2 + √5)

= 2 - √3 + √5 + √3 - 2 - √5

= 0

So, 1/(2 + √3) + 2/(√5 - √3) + 1/(2 - √5) = 0

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Answer 2

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