Question

how to solve this- find a and b in 3+square root of 5÷ 3- square root of 5 = a+b ×square root of 5

Answer 1

3+√5/3-√5=a+b×√5
(3+√5)^2/3^2-(√5)^2=√5a+√5b
9+6√5+5/9-5=√5a+√5b
14+6√5/4=√5a+√5b

Answer 2

Hiii friend,


3+✓5/3-✓5 = A + B✓5


LHS = 3+✓5/3-✓5



Rationalizing the denominator 3-✓5 we get,


3+✓5/3-✓5 × 3+✓5/3+✓5


=> (3+✓5)²/(3-✓5)(3+✓5)²


=> (3)² + (✓5)² + 2 × 6 × ✓5 / (3)² - (✓5)²


=> 9 + 5 + 12✓5/ 9 -5

=> 14 + 12✓5/4


=> 2(7+6✓5)/4


=> 7 + 6✓5/2


Now,


LHS = RHS


7+6✓5/2 = A+B✓5


Clearly ,


A = 7/2 and B = 6/2 = 3




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