Question

Find the value of a and b if a+8√5b=8+√5/8-√5​

Answer 1

Answer:

GIVEN

if a+8√5b=8+√5/8-√5+8-√5/8+√5

RHS

= 8 + (√5 / 8) - √5 + 8 - (√5 / 8) + √5

MAKE IT EQUAL TO a + 8√5b

8 + (√5 / 8) - √5 + 8 - (√5 / 8) + √5 = a + 8√5b

LCM is 8

(64 + √5 - 8√5 + 64 - √5 + 8√5) / 8 = a + 8√5b

128 / 8 = a + 8√5b

16 = a + 8√5b

Can be written as

16 + (8√5) x0 = a + 8√5b

Therefore, a = 16 & b = 0

Step-by-step explanation:

Answer 2

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

$= \frac{(8 + \sqrt{5})(8 + \sqrt{5} ) }{(8 - \sqrt{5})(8 + \sqrt{5} )}$

$= \frac{64 + 16 \sqrt{5} + 5}{64 - 5}$

$= \frac{64 + 16 \sqrt{5} + 5 }{59}$