Question

Find a and b if √13-√7/√13+√7=a-√91b. please answer quick​

Answer 1

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here is your answer (Note text enclosed in "" are comments need to be ignore if u know it only for better understanding)

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√13-√7/√13+√7=a-√91b (Given)

By taking LHS

√13-√7/√13+√7

By rationalising ("rationalising denominator to simplify removing roots")

√13-√7/√13+√7 X √13-√7/√13-√7   ("multiplying and dividing by√13-√7 ")

⇒(√13-√7)²/13-7         {(a+b)(a-b)=(a²-b²)}

⇒13+7+2√91/6            {(a-b)²=a²+b²-2ab}

⇒20+2√91/6

⇒20/6+2√91/6              ("Separately divide")

⇒10/3+1/3√91        

On comparing with RHS  i.e.a-√91b

we get

a=10/3 and b=1/3

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Hope it helps

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