Question

Find the value of a and b if 7+√5/7-√5 - 7+-√5/7+√5 =a +7/11√5b

Answer 1

Hello dear ...

Your Solution is given below
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Question Given =
$\frac{7 + \sqrt{5} }{7 - \sqrt{5} } - \frac{7 - \sqrt{5} }{7 + \sqrt{5} } = a + \frac{7}{11} \sqrt{5b}$


$= > \frac{(7 + \sqrt{5} {)}^{2} - (7 - \sqrt{5} {)}^{2} }{(7 - \sqrt{5} )(7 + \sqrt{5}) } = a + \frac{7}{11} \sqrt{5} b \\ \\ = > \frac{(7 {)}^{2} + ( \sqrt{5} {)}^{2} + (2.7. \sqrt{5} ) -(7 {)}^{2} + ( \sqrt{5} {)}^{2} - 2.7. \sqrt{5}) }{ {7}^{2} - ( \sqrt{5} {)}^{2} } \\ = a + \frac{7}{11} \sqrt{5} b$
using formula ÷

{(a+b)² = a²+2ab+b²}
{(a-b)² = a² -2ab + b²}
{(a-b)(a+b)= a² - b²}


$= > \frac{49 + 5 + 14 \sqrt{5} - 49 - 5 + 14 \sqrt{5} }{49 - 5} = a + \frac{7}{11} \sqrt{5}b \\ \\ = > \frac{28 \sqrt{5} }{44} = a + \frac{7}{11} \sqrt{5}b \\ \\ = > \frac{7}{11} \sqrt{5} = a + \frac{7}{11} \sqrt{5} b \\ \\ = > 0 + \frac{7}{11} \sqrt{5} = a + \frac{7}{11} \sqrt{5}b$

on comparing both sides , we get

=> a = 0 , b = 1 answer.

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Hope it's helps you.
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