Find the value of a and b in x2–16x+a=(x+b)2
Compare coefficients in x2–16x+a=(x+b)2 to find value of a and b
x2–16x+a=(x+b)2
We will expand (x+b)2using the identity
(a+b)2=a2+2ab+b2
We get the equation as
x2–16x+a=x2+2bx+b2
On equating the coefficients on L.H.S and R.H.S
-16=2b
b=-162
b=-8
and
a=b2a=(-8)2a=64
Hence a=64 and b=-8