Question

8 + root 5 by 8 minus root 5 + 8 minus root 5 by 8 + root 5 is equal to a + 8 root 5 b​

Answer 1

Answer: a= 138/59, b=0

Step-by-step explanation:

Here is your answer .....hope it helps

Answer 2

Complete question is 8 + root 5 by 8 minus root 5 + 8 minus root 5 by 8 + root 5 is equal to a + 8 root 5 b then find the value of a and b.

Answer:

Required value of a is (138/59) and value of b is 0.

Step-by-step explanation:

Given,

$\frac{8 + \sqrt{5} }{8 - \sqrt{5} } + \frac{8 - \sqrt{5} }{8 + \sqrt{5} } = a + b \times 8 \sqrt{5} .......(1)$

First we take,

$\frac{8 + \sqrt{5} }{8 - \sqrt{5} }$

Multiplying denominator and nemerator by

$(8 + \sqrt{5} )$ and get,

$\frac{(8 + \sqrt{5} )(8 + \sqrt{5}) }{(8 - \sqrt{5} )(8 + \sqrt{5}) } = \frac{ {(8 + \sqrt{5} )}^{2} }{ {8}^{2} - { \sqrt{5} }^{2} } = \frac{64 + 16 \sqrt{5 } + 5 }{64 - 5} = \frac{69 + 16 \sqrt{5} }{59}$

Second we take,

$\frac{8 - \sqrt{5} }{8 + \sqrt{5} }$

Multiplying denominator and nemerator by

$8 - \sqrt{5}$ and get,

$\frac{(8 - \sqrt{5})(8 - \sqrt{5}) }{(8 + \sqrt{5} )(8 - \sqrt{5} )} = \frac{ {(8 - \sqrt{5}) }^{2} }{ {8}^{2} - { \sqrt{5} }^{2} } = \frac{64 - 16 \sqrt{5} + 5}{64 - 5} = \frac{69 - 16 \sqrt{5} }{59}$

From equation (1),

$\frac{69 + 16 \sqrt{5} }{59} + \frac{69 - 16 \sqrt{5} }{59} = a + 8 \sqrt{5} b$

$\frac{69 - 16 \sqrt{5} + 69 + 16 \sqrt{5} }{59} = a + 8 \sqrt{5} b$

$\frac{138}{59} = a + 8 \sqrt{5} b$

Comparing both side and get,

$a = \frac{138}{59}$

and b=0

Here applied formulas are

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

${(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

${x}^{2} - {y}^{2} = (x + y)(x - y)$