# The product of the square of two numbers is 225. What are the numbers?

justaguide | College Teacher | (Level 2) Distinguished Educator

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We have only been given that the product of the squares of two numbers is equal to 225. If the two numbers are x and y, we have x^2*y^2 = 225. Now it is not possible to find the values of x and y with the information given as we have two variables but we can only create one equation.

If we assume that x and y are integers, then we can find the values of x and y. We have x^2*y^2 = 225, or (x*y)^2 = 15^2.

So x*y = +15 or -15. Therefore for any x, y = -15/x or +15/x. Now, we find the pairs of integers (-1 , -15), (-3, -5), (1, 15), (3, 5), (-1 , 15), (-3, 5), (1, -15) and (3, -5) satisfy the relation.

neela | High School Teacher | (Level 3) Valedictorian

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The product of squares of two numbers are 225.To find the numbers.

Solutions:

Let x^2*y^2 = 225.

Subtract  225 from both sides:

x^2y^2-225 = 0.

(xy-15)(xy+15) = 0

Therefore xy -15. Or xy = 15.

Therefore (x,y) = (1,15), (x,y) = (15,1), (x,y) = (3,5), (x,y) = (5,3) are some solutions.

xy = 15 is actually  a hyperbola and for any x = k,  y = 15/k is a solution.

Similarly xy = -15 is also hyperbola. (x,y) = (1,-15) , (x,y) = (-1 , 15) , (x,y) = (3,-5) , (x,y) = (-3 , 5) etc are some solutions.

For any point x = t, y= -15/t is a solution and is on the hyperbola.