Given that $a^2 - b^2 = 45$ and $a - b = 9$ , what is the average of $a$ and $b$ ?

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7.5

2.5

Correct

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Explanation

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Official Explanation

Official

We start with the equation

a^2 - b^2 = 45

. This can be factored as

(a - b)(a + b) = 45

. Since we know that

a - b = 9

, we can substitute this into the equation: [m]9(a +…

Comments

subhamJan 31, 2024

finally understood this

UdaySep 1, 2024

thanks!

What this question tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.