GreenlightTestPrep wrote:
x = ∜(x³ + 6x²)
Quantity A |
Quantity B |
sum of all possible values of x |
1 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Given: x = ∜(x³ + 6x²)
Raise both sides to the power of 4 to get: x⁴ = x³ + 6x²
Rewrite equation as follows: x⁴ - x³ - 6x² = 0
Factor to get: x²(x² - x - 6) = 0
Factor more to get: x²(x - 3)(x + 2) = 0
This means x² = 0, (x - 3) = 0, or (x + 2) = 0
So, the possible solutions are x = 0, x = 3 and x = -2
IMPORTANT: At this point, we should plug each answer choice back into the equation to identify any possible
extraneous roots.
Test x = 0. We get: 0 = ∜(0³ + 6*0²) = ∜(0). WORKS
Test x = 3. We get: 3 = ∜(3³ + 6*3²) = ∜(81). WORKS
Test x = -2. We get: -2 = ∜(-2³ + 6*-2²) = ∜(16). DOESN’T work.
So, the only VALID solutions are x = 0 and x = 3
So, the SUM of all possible values of x = 0 + 3 = 3
We get:
QUANTITY A: 3
QUANTITY B: 1
Answer: A
Cheers,
Brent