Question

if x²-20x+a=(x-b)² , find the value of a and b.........................

Answer 1

x²-20x+a=(x-b)²
⇒x²-20x-a=x²+b²-2bx
⇒x²-x²-20x-a=b²-2bx
⇒b²-2bx+20x-a=0
⇒b²-x(2b-20)-a=0
for this quadratic equation:
Discriminant D= B²-4AC
And A=1'B=2b-20;C=-a
Then;
(2b-20)²4a=0
⇒b²+100-20b-a=0
⇒10²+b(b+20)-a=0
Now again for the quadratic equation th 
Discriminant D=B²-4AC
B=10,A=1,C=-a
So
(b+20)²+4a=0
If i will type the complete solution it will go very long.
The value of a =12
and The value of b=-8

Answer 2

Expand RHS to get (x+b)^2 = x^2 + 2xb + b^2

Now compare LHS and RHS:

x^2 - 20x + a = x^2 + 2xb + b^2

Compare like terms, we have 2b = -20 => b = -10

and b^2 = a => a = -10^2 = 100