Question

Hey guys solve the question plzz​

Answer 1

Given :-

{ (7 + 3√5)/(3 + √5) } - { (7 - 3√5)/(3-√5) } = a + b√5

Solving LHS:-

By taking L.C.M , we have :-

{ (7 + 3√5)(3 - √5) - (7 - 3√5)(3 + √5) } / (3+ √5)(3 - √5)

=> { (21 - 7√5 + 9√5 - 15) - (21 + 7√5 - 9√5 -15) } / (3)² - (√5)²

[ By identity (a+b)(a-b) = a² - b² ]

=> { 6 + 2√5 - ( 6 - 2√5 ) } / (9 - 5)

=> { 6 + 2√5 -6 + 2√5 } / 4

=> 4√5/4

=> √5

Now ,

LHS = RHS

√5 = a + b√5

Here , We can see ,

a = 0

and

b = 1

Solved...

Hope it helped you...