Question

Pls don't give me irrevalant ans pls give proper ans​

Answer 1

Step-by-step explanation:

Question:-

Find the Value of a and b if:-

$\sf \dfrac{7 + \sqrt{5} }{7 - \sqrt{5} } - \dfrac{7 - \sqrt{5} }{7 + \sqrt{5} } = a + \dfrac{7}{11} \sqrt{5} \: b$

Solution:-

$\sf LHS = \dfrac{7 + \sqrt{5} }{7 - \sqrt{5} } - \dfrac{7 - \sqrt{5} }{7 + \sqrt{5} }$

$\sf\underline{ Rationalising \: the \: denominator:-}$

$\sf = \Bigg(\dfrac{7 + \sqrt{5} }{7 - \sqrt{5} } \times \dfrac{7 + \sqrt{5} }{7 + \sqrt{5} } \Bigg) - \Bigg(\dfrac{7 - \sqrt{5} }{7 + \sqrt{5} } \times \dfrac{7 - \sqrt{5} }{7 - \sqrt{5} } \Bigg)$

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

$\sf = \dfrac{ {7}^{2} + {( \sqrt{5}) }^{2} + 2(7)( \sqrt{5}) }{49 - 5 } - \dfrac{ {7}^{2} + {( \sqrt{5}) }^{2} - 2(7)( \sqrt{5}) }{49 - 5 }$

$\sf = \dfrac{ 49 + 5+ 14 \sqrt{5} }{44} - \dfrac{ 49+ 5 -14\sqrt{5} }{44 }$

$\sf = \dfrac{54+ 14 \sqrt{5} }{44} - \dfrac{54 -14\sqrt{5} }{44 }$

$\sf = \dfrac{54+ 14 \sqrt{5} - (54 - 14 \sqrt{5} )}{44}$

$\sf = \dfrac{54+ 14 \sqrt{5} - 54 + 14 \sqrt{5} }{44}$

$\sf = \dfrac{ 2(14 \sqrt{5}) }{44}= \dfrac{ 28 \sqrt{5} }{44}$

$\sf = \dfrac{ 7 \sqrt{5} }{11} = 0 + \dfrac{ 7 \sqrt{5} }{11}$

$\sf comparing \: \: 0 + \dfrac{ 7 \sqrt{5} }{11} \: \: with \: \: a + \dfrac{7 }{11} \sqrt{5} \: b$

$\sf a = 0 \: \: , \: b = 1$

$\Large \dashrightarrow \underline{ \boxed{\therefore\textsf{ \textbf{a = 0 \: , \: \: b = 1}} }}$

Answer 2

a=0,b=1

Hope it helps. ....