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.

Explanation:

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 .