Final answer:
To find the values of a and b in the given identity x² - 12x + 10 = (x + a)² + b, it is important to compare the coefficients of the terms and equate them to the standard form of the square of a binomial. By doing this, we can determine that a = -6 and b = -26.
Step-by-step explanation:
To find the values of a and b in the given identity, we can compare the given equation with the standard form of the square of a binomial, which is (x + a)² = x² + 2ax + a². By comparing the coefficients of the terms, we can see that -12x is equivalent to 2ax and 10 is equivalent to a² + b.
From this comparison, we can deduce that a = -6 (since 2ax = -12x) and b = 10 - a² = 10 - 36 = -26. Therefore, the values of a and b are -6 and -26, respectively.
Learn more about values of a and b