Question

Please, help me it's urgent.

FIND : ROOT (a^2+b^2)^2 - (a^2-b^2)^2

Answer 1

Let (x+iy)2=4ab−2i(a2−b2)

Comparing the real and imaginary terms, 

x2−y2=4ab----------------------------------------(i)

xy=a2−b2---------------------------------------(ii)

Comparing the magnitude, 

x2+y2=4a4+4b4+8a2b2 

⇒x2+y2=2a2+2b2   -(iii)

Solving (i) and (iii),

x2=a2+b2+2ab and y2=a2+b2−2ab

Hence, 

x=a+b , y=a−b

or x=−(a+b) , y=b−a

Hence, option B is correct

Answer 2

Let me give you a contradiction.

Let a=1a=1

and b=1b=1

Now, L.H.S. ,

a2+b2−−−−−−√=12+12−−−−−−√=2–√a2+b2=12+12=2

and R.H.S. ,

a+b=1+1=2a+b=1+1=2

Clearly,

2–√≠22≠2

Hence,

a2+b2−−−−−−√≠a+b