Question

root 5 +root 3 by 2 root 5 _ 3 root 3 = a_b root 15​

Answer 1

Answer:

the question is not clear

Answer 2

GIVEN :-

• (√5 + √3)/(2√5 - 3√3) = a - b√15.

TO FIND :-

• The value of a and b.

SOLUTION :-

$\\ : \implies \displaystyle \sf \: \frac{ \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - 3 \sqrt{3} } = a - b \sqrt{15}$

$: \implies \displaystyle \sf \: \dfrac{\big( \sqrt{5} + \sqrt{3} \big) \big( 2 \sqrt{5} + 3\sqrt{3} \big)}{ \big( 2 \sqrt{5} - 3\sqrt{3} \big)\big( 2 \sqrt{5} + 3\sqrt{3} \big) } = a - b \sqrt{15}$

$: \implies \displaystyle \sf \: \frac{ \sqrt{5} \big(2 \sqrt{5} + 3 \sqrt{3} \big) + \sqrt{3} \big(2 \sqrt{5} + 3 \sqrt{3} \big)}{ \big(2 \sqrt{5} \big) ^{2} - \big(3 \sqrt{3} \big) ^{2} } = a - b \sqrt{15}$

$: \implies \displaystyle \sf \: \frac{2 \sqrt{25} + 3 \sqrt{15} + 2 \sqrt{15} + 3 \sqrt{9} }{4 \sqrt{25} - 9 \sqrt{9} } = a - b \sqrt{15}$

$: \implies \displaystyle \sf \: \frac{10 + 3 \sqrt{15} + 2 \sqrt{15} + 9}{20 - 27} = a - b \sqrt{15}$

$: \implies \displaystyle \sf \: \frac{10 + 5 \sqrt{15} + 9}{ - 7} = a - b \sqrt{15}$

$: \implies \displaystyle \sf \: \frac{19 + 5 \sqrt{15} }{ - 7} = a - b \sqrt{15}$

$: \implies \displaystyle \sf \: \frac{ - (19 + 5 \sqrt{15} )}{7} = a - b \sqrt{15}$

$: \implies \displaystyle \sf \: \frac{ - 19 - 5 \sqrt{15} }{7} = a - b \sqrt{15}$

$: \implies \displaystyle \sf \: \frac{ - 19}{7} - \frac{5}{7} \sqrt{15} = a - b \sqrt{15}$

On camparing Both the sides we get,

$\\ \\ : \implies \underline{ \boxed{ \displaystyle \sf \: \bold{ a = \frac{ - 19}{7} \: , \: b = \frac{5}{7} }}}$