Given that $b = a + 5$ , which of the following values of $x$ minimizes the expression $(x - a)^2 + (x - b)^2$ ?

Correct answer marked below

a + \frac{5}{3}

a + 3

a + 1

a + \frac{5}{2}

Correct

a + \frac{5}{4}

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Explanation

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Official Explanation

Official

To find the minimum of the expression

(x - a)^2 + (x - b)^2

, we can rewrite it as

(x - a)^2 + (x - (a + 5))^2

. This simplifies to…

Comments

MuhammadMar 23, 2025

Great!

KeshavMay 9, 2024

thanks for posting

KushalOct 5, 2024

cheers!

What this question tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).