Solve the quadratic equation : x²-2ax+(a²-b²)=0 . . .

Question : Solve the quadratic equation : x²-2ax+(a²-b²)=0 for x.

Doubt by CBSE 

Solution :

By Factorisation Method

x²-2ax+(a²-b²)=0

x²-[(a+b)+(a-b)]x+(a²-b²)=0
x²-(a+b)x-(a-b)x+(a²-b²)=0
x[x-(a+b)]-(a-b)[x-(a+b)]=0
[x-(a+b)][x-(a-b)]=0
[x-(a+b)] = 0 & [x-(a-b)] = 0
x=(a+b) & x=(a-b) 

By Quadratic Formula

x²-2ax+(a²-b²)=0
A=1

B=-2a
C=(a²-b²)

D=B²-4AC
D=(-2a)²-4(1)(a²-b²)
D=4a²-4(a²-b²)
D=4a²-4a²+4b²
D=4b²

∵ D>0
∴ Roots are real and distinct. 

Hence, x=(a+b) & x=(a-b)