Question

Please solve the above questions... Recommended

Answer 1

Given that,
x=√(a/b)+√(b/a)

x=√a/√b+√b/√a

x=[√(a²)+√(b²)]/√ab

x=(a+b)/√ab.......................................1

x²-4=(a+b)²/ab-4

x²-4=[a²+b²+2ab-4ab]/ab

x²-4=(a-b)²/ab........................................2
We have,
=√(x²-4)/[x+√(x²-4)]

=√[(a-b)²/ab]/[(a+b)/√ab+√(a-b)²/ab]

=[(a-b)/√ab]/[(a+b)/√ab+(a-b)/√ab]

=[(a-b)/√ab]/[2a/√ab]

=(a-b)/√ab×√ab/(2a)

=(a-b)/2a.

Hence value of √(x²-4)/[x+√(x²-4)]=(a-b)/2a