Question

2/root 3+root 5+5/root 3 - root 5= a root 3+b root 5

Answer 1

Hi ,

LHS = 2/( √3 + √5 ) + 5/( √3 - √5 )

= [ 2(√3-√5)+5(√3+√5) ]/[(√3+√5)(√3-√5)]

= [2√3-2√5+5√3+5√5]/[ ( √3 )² - ( √5 )² ]

= ( 7√3 + 3√5 )/( 3 - 5 )

= ( 7√3 + 3√5 )/( -2 )

= ( -7/2 ) √3 + ( -3/2 )√5----( 1 )

= a√3 + b√5 ---------( 2 )

Compare equations ( 1 ) and ( 2 ) , we get

a = -7/2 ,

b = - 3/2

I hope this helps you.

: )

Answer 2

Hiiii friend,

=> 2/(✓3+✓5) + 5/(✓3-✓5)

=> 2(✓3-✓5)+5(✓3+✓5)/(✓3+✓5)(✓3-✓5)

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

=> 7✓3 +3 ✓5/(-2)

=> 7✓3/(-2) + 3✓5/(-2)

Now,

LHS = RHS

7✓3 + 3✓5/(-2) = A✓3 + B✓5

Clearly -7✓3 is instead of A and -3/✓2 is instead of B.

So,

A = -7/(2) and B = -3/(2)

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