16Hit1600
Advanced MathVery hardSum of solutions of an exponential quadratic

Advanced Math practice question

The equation 3^(2x) − 10·3ˣ + 9 = 0 has two solutions. What is their sum?

Answer: 2

Let u = 3ˣ: u² − 10u + 9 = (u − 1)(u − 9) = 0, so 3ˣ = 1 or 3ˣ = 9, giving x = 0 or x = 2. The sum is 2.

Common wrong answers

If you answered 3
3 adds x = 2 and x = 1 from misreading 3ˣ = 1 as x = 1.
If you answered 9
9 is one value of u.
If you answered 10
10 is the sum of the values of u, not of x.

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