Answered

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The sum of two numbers is 3 and the sum of their squares is 29. what are the numbers?

Sagot :

Explanation:

[tex]x + y = 3[/tex]

[tex] {x}^{2} + {y}^{2} = 29[/tex]

[tex]x = 3 - y[/tex]

[tex](3 - y) {}^{2} + {y}^{2} = 29[/tex]

[tex] {y}^{2} - 6y + 9 + {y}^{2} = 29[/tex]

[tex]2 {y}^{2} - 6y + 9 = 29[/tex]

[tex]2 {y}^{2} - 6y = 20[/tex]

[tex] {y}^{2} - 3y = 10[/tex]

[tex] {y}^{2} - 3y - 10 = 0[/tex]

[tex](y - 5)(y + 2) = 0[/tex]

[tex]y = 5[/tex]

or

[tex]y = - 2[/tex]

Plug this back in we get either that

[tex]5 + x = 3[/tex]

[tex]x = - 2[/tex]

or

[tex]x = 5[/tex]

So the numbers are

-2 and 5.

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