Question

PLEASE SOLVE THIS QUESTION. WITH FULL PROCEDURE. NEED URGENTLY. PLEASE SOLVE IT FAST.
question 5 part 3​

Answer 1

Step-by-step explanation:

We have,

$\frac{7 + \sqrt{5} }{7 - \sqrt{5} } - \frac{7 - \sqrt{5} }{7 + \sqrt{5} } = a + \frac{7}{11} b \sqrt{5}$

$\implies\frac{(7 + \sqrt{5})^{2} - (7 - \sqrt{5}) ^{2} }{(7 - \sqrt{5} )(7 + \sqrt{5} )} = a + \frac{7}{11} b \sqrt{5}$

$\implies\frac{(7 + \sqrt{5})^{2} - (7 - \sqrt{5}) ^{2} }{(7 )^{2} - ( \sqrt{5} )^{2} } = a + \frac{7}{11} b \sqrt{5}$

$\implies\frac{4.7. \sqrt{5} }{49 - 5 } = a + \frac{7}{11} b \sqrt{5}$

$\implies\frac{4.7. \sqrt{5} }{44} = a + \frac{7}{11} b \sqrt{5}$

$\implies\frac{7\sqrt{5} }{11} = a + \frac{7}{11} b \sqrt{5}$

$\implies(0 )+ \frac{7}{11}(1) \sqrt{5} = a + \frac{7}{11} b \sqrt{5}$

On comparing both sides,

we get, $a=0 \: \& \: b=1$