If $a+8\sqrt{5}b=8+(\frac{\sqrt{5}}{8})-\sqrt{5}+8-(\frac{\sqrt{5}}{8})+\sqrt{5}$, find a and b.

Given : 

The given expression is, $a+8\sqrt{5}b=8+(\frac{\sqrt{5}}{8})-\sqrt{5}+8-(\frac{\sqrt{5}}{8})+\sqrt{5}$

To Find :

We have to find the values of a and b.

Solution :

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

Rewrite the given expression, 

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

[$\sqrt{5}-\sqrt{5}=0$ ; $(\frac{\sqrt{5}}{8})-(\frac{\sqrt{5}}{8}) = 0$]

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

$a+8\sqrt{5}b=16$

This can be written as,

$a+8\sqrt{5}b=16 + 8\sqrt{5} (0)$

Compare the values ,

a = 16  

b  =  0

Therefore, the values of a and b are 16, 0.

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Updated on: 10-Oct-2022

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