Question

√3+√2/√3-√2=a+b√6 please tell the answer with explanation step by step

Answer 1

Heya !!

✓3 + ✓2 / ✓3 - ✓2 = A + B✓6



LHS = ✓3 + ✓2 / ✓3 - ✓2


=> ( ✓3 + ✓2 ) / ( ✓3 - ✓2 ) × ( ✓3 + ✓2 ) / ( ✓3 + ✓2)




=> ( ✓3 + ✓2 )² / ( ✓3 - ✓2 ) ( ✓3 + ✓2 )


=> (✓3)² + (✓2)² + 2✓3 × ✓2 )/ ( ✓3)² - (✓2)²



=> 3 + 2 + 2✓6 / 3 - 2


=> 5 + 2✓6 / 1


=> 5 + 2✓6


Now,


LHS = RHS


5 + 2✓6 = A + B✓6



Clearly,

A = 5 and B = 2.

Answer 2

I can only give a example please experience and try to under stand (√a+√b)=(√a)square -(√b)square =a-b