Find the value of a and b in x^2 - 16x + a = (x + b)^2

Given

x2 – 16x+a=(x+b)2

Find out

We have to find the values of a and b

Solution

x2 – 16x+a=(x+b)2

We will expand (x+b)2 using the identity (a+b)2

We get the equation as

x2 – 16x+a=x2 +2bx+b2

On equating the coefficients on LHS and RHS

-16=2b

b=-16/2

b=-8

Again on equating coefficients

a=b2

a=(-8)2

a=64

Hence, a=64 and b=-8

Answer

In the given equation x2 – 16x+a=(x+b)2 the value of a is 64 and b is -8

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