Question

√a=√b+√c then (a+b-c)^2÷(a-b+c)^2 is equal to

Answer 1

Hi ,

It is given that ,

√a = √b + √c ----( 1 )

square both sides of the equation ,

a = b + c + 2√bc ---( 2 )

Now ,

( a + b - c )² / ( a - b + c )²

= [ ( a + b - c )/ ( a - b + c ) ]²

= [( b + c + 2√bc + b - c )/( b + c + 2√bc -b + c)]²

= [ ( 2b + 2√bc )/( 2c + 2√bc )]²

= { [2√b(√b + √c )]/ [2√c ( √c + √b )] }²

after cancellation ,

= ( √b / √c )²

= b/c

I hope this helps you.

: )