Question

The sum of the squares of two numbers is 18. the product of the two numbers is 9. find the numbers.

Answer 1

Answer:

x=3 y=3

Step-by-step explanation:

The sum of the squares of two numbers is 18, and the product of those two numbers is 9, you just need to create an equation:

So the sum of the squares is 18, the first number will be represented as X and the second as Y:

$x^{2}+ y^{2} =18$

And the other one is that the product of the two numbers is 9:

$xy=9$

We have a system of equations here, we clear X from the first one:

$x=\frac{9}{y}$

And instert that value of x in the first one:

$x^{2}+ y^{2} =18\\(\frac{9}{y} )^{2}+ y^{2} =18\\81=y^2(18-y^2)\\y^4-18y^2+81=0\\(y^2-9)(y^2-9)=0\\Y^2-9=0\\y^2=9\\y=3$

By solving this equation we get that the first number is 3.

The second number is solved by inserting the value of Y into one of the equations, in this case we will use the second:

$xy=9\\x=\frac{9}{y} \\x=\frac{9}{3} \\x=3$

So we get that x and y are both 3.

Answer 2

A graph shows the two numbers are either (3, 3) or (-3, -3).