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

User Juherr
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2 Answers

4 votes

Answer:

x=3 y=3

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=(9)/(y)

And instert that value of x in the first one:


x^(2)+ y^(2) =18\\((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=(9)/(y) \\x=(9)/(3) \\x=3

So we get that x and y are both 3.

User Klenwell
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9.2k points
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A graph shows the two numbers are either (3, 3) or (-3, -3).
The sum of the squares of two numbers is 18. the product of the two numbers is 9. find-example-1
User KHALDOUN
by
8.4k points

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