Question

Find the value of a and b​

Answer 1

Answer:

0 , 1.

Step-by-step explanation:

Simplifying LHS :

$\implies \dfrac{ 7 + \sqrt{5} }{ 7 - \sqrt{5} } - \dfrac{ 7 - \sqrt{5} }{ 7 + \sqrt{5}} \\ \\ \\ \implies \dfrac{ (7 + \sqrt{5} ) {}^{2} - (7 - \sqrt{5} ) {}^{2} }{ (7 - \sqrt{5} )(7 + \sqrt{5} )}$

Using :

( a + b )^2 = a^2 + b^2 + 2ab

( a - b )^2 = a^2 + b^2 - 2ab

( a + b )( a - b ) = a^2 - b^2

$\implies \dfrac{ (7 {}^{2} + (\sqrt{5} {)}^{2} + 14 \sqrt{5}) - (7 {}^{2} + ( \sqrt{5} ) {}^{2} - 14 \sqrt{5}) }{ (7 - \sqrt{5})(7 + \sqrt{5} {)} } \\ \\ \\ \implies \dfrac{ (7 {}^{2} + (\sqrt{5} {)}^{2} + 14 \sqrt{5}) - 7 {}^{2} - ( \sqrt{5} ) {}^{2} + 14 \sqrt{5}) }{ (7) {}^{2} - ( \sqrt{5}) {}^{2} } \\ \\ \\ \implies \dfrac{28 \sqrt{5} }{49 - 5}$

= > 28√5 / 44

= > 0 + 7√5 / 11

Comparing both sides :

= > a = 0

= > 7√5 / 11 = 7√5 b / 11

= > b = 1

Answer 2

Step-by-step explanation:

Aloha !

7+√5/7-√5 - 7-√5/7+√5

(7+√5)(7+√5)-(7-√5)(7-√5) ÷ 7-√5 - 7+√5

(7+√5)²-(7-√5)²÷ 7-√5 -7 +√5

(49+25+14√5) - (49+25-14√5)÷ 49-5

14√5+14√5÷44

28/44×√5

7/11×√5

Comparing with a+7/11× √5 b

Here a=0 and b= 1.

Thank you

@ Twilight Astro ✌️☺️♥️