Question

(√5-√3)(3√5-5√3)=a+b√15find value of a and b

Answer 1

$\large \tt AHOY!! \:$

given :- (√5 - √3)(3√5 - 5√3) = a + b√15

L.H.S :-

= (√5 - √3)(3√5 - 5√3)

= √5(3√5 - 5√3) - √3(3√5 - 5√3)

= 3(5) - 5√15 - 3√15 + 5(3)

= 15 - 8√15 + 15

= 30 - 8√15

R.H.S :-

= a + b√15

comparing L.H.S with R.H.S :-

=> 30 - 8√15 = a + b√15

=> 30 + (- 8√15) = a + b√15

therefore a = 30 and b = -8

$\large \tt HOPE \: THIS \: HELPS!!$