I made it simpler, 2 variables, 2 unknowns

Algebra Level 1

Let x and y be positive integers.

You are given the following 2 equations.

1) $x + y = 11$

2) $xy^{2} = 72$

What is the numerical value of $x^{3}y$ ?

The answer is 1536.

1 solution

Denton Young
Jul 10, 2015

since x + y = 11, x = 11 - y

substituting, $y^{2}(11 - y)$ = 72

72 = 8 * 9 = 8 * $3^{2}$

so y = 3, therefore x = 11-3 = 8

$8^3$ * 3 = 1536

$y=3$ is not the only solution. Because $y^2(11-y) - 72 = 0$ is a cubic equation, then it has at most 3 roots. factoring out $(y-3)$ gives $y = 4 \pm 2 \sqrt{10}$ as the other two roots. So there are another two values of $x^3 y$ .

You should clarify in your question that you're only looking for integers of $x$ and $y$ , else there will be 3 distinct answers.

Pi Han Goh - 5 years, 11 months ago

Okay, it's fixed.

Denton Young - 5 years, 11 months ago

Good point. Will fix.

Denton Young - 5 years, 11 months ago

I made it simpler, 2 variables, 2 unknowns

The answer is 1536.

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