Question

If 2/√3+√5 + 5/√3-√5 = a√3+b√5, find a and b.​

Answer 1

2/(✓3 + ✓5) + 5/(✓3 - ✓5) = a✓3 + b✓5

take lcm

{2(✓3 - ✓5) + 5(✓3 + ✓5) } / (✓3 - ✓5)(✓3 + ✓5) =

a✓3 + b✓5

(2✓3 - 2✓5 + 5✓3 + 5✓5) / (3 - 5) = a✓3 + b✓5

(7✓3 + 3✓5) / -2 = a✓3 + b✓5

-7✓3/2 - 3✓5/2 = a✓3 + b✓5

compare

a✓3 = -7✓3/2

a = -7/2

b✓5 = - 3✓5/2

b = -3/2