Question

If a and b be two rational number find the value of a and b in the following. √5+√3/√5-√3 = a+b√15

Answer 1

Hii friend,

✓5 + ✓3 / ✓5 - ✓3 = a + b✓15

LHS = ✓5+✓3/✓5-✓3

=> ✓5 + ✓3 / ✓5 - ✓3 × ✓5 + ✓3 / ✓5 + ✓3.

=> (✓5+✓3)(✓5+✓3)/(5-✓3)(✓5+✓3).


We know that,

(A+B)² = A²+B²+2×A×B

=> (✓5+✓3)²/ (✓5)²-(✓3)²

=> (✓5)² + (✓3)² + 2 × ✓5 × ✓3/5 - 2

=> 5+3+2✓15/2

=> 8+2✓15/2

=> 2(4+✓15)2 = 4+✓15

LHS = RHS

4+✓15 = a+b✓15

Therefore,

A = 4 and B = 1.

HOPE IT WILL HELP YOU..... :-)