Question

if 2 minus root 5 upon 2 + 3 root 5 equal to a root 5 + b find a and b. ( ques 9 on image)​

Answer 1

Answer:

$\frac{2 - \sqrt{5} }{2 + 3 \sqrt{5} } = a \sqrt{5} + b \\ \frac{2 - \sqrt{5} }{2 + 3 \sqrt{5} } \times \frac{2 - 3 \sqrt{5} }{2 - 3 \sqrt{5} } = a \sqrt{5} + b \\ \frac{ 4 - 6 \sqrt{5 } - 2 \sqrt{5 } + 3 \times 5 }{4 - 45} =a \sqrt{5} + b \\ \frac{21 - 8 \sqrt{5} }{ - 41} = a \sqrt{5} + b \\ \frac{8 \sqrt{5} - 21}{41} = a \sqrt{5} -(- b )\\ thus \: \: a \sqrt{5} \: = \frac{8 \sqrt{5} }{41} \: \: \\ ie. \: \: \: \: a = \frac{8}{41} \\ and \: b = \frac{ 21}{41}$

Answer 2

Answer:

hope it's helpfull

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