The product of the square of two numbers is 225. What are the numbers?
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.
The product of squares of two numbers are 225.To find the numbers.
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.