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frutty [35]
3 years ago
9

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

Mathematics
2 answers:
OLEGan [10]3 years ago
8 0

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.

zhuklara [117]3 years ago
4 0
A graph shows the two numbers are either (3, 3) or (-3, -3).

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