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Find the value of a and b in x2 - 16x + a = (x + b)2 .
The coefficients of two polynomials can be equal and identical for each different type of term.
Answer: The value of a is 64 and the value of b is 8 for x2 - 16x + a = (x + b)2.
Let's find a and b.
Given, x2 - 16x + a = (x + b)2
By expanding the RHS using (a + b)2 = a2 + 2ab + b2, we get
x2 - 16x + a = x2 + 2xb + b2
On solving this equation, we get
- 16x + a = 2xb + b2 --- (1)
By equating the coefficients of 'x' in the equation (1), we get
- 16 = 2 b
b = - 16 / 2
b = - 8
By equating the values of constants from in the equation (1), we get
a = b2
a = (- 8)2 (Using value of b)
a = 64
Thus, the value of a is 64 and the value of b is 8 for x2 - 16x + a = (x + b)2 .