# The sum of two numbers is 9 and the sum of their squares is 261. How do you find the numbers?

Either 15 and -6 or -6 and 15.

Let one number be x, then other's is 9 - x.

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Use substitution by solving for one variable in the first equation and substituting this variable into the second equation:

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Let ( x ) and ( y ) represent the two numbers. Given that the sum of the two numbers is 9, we have the equation ( x + y = 9 ). Additionally, since the sum of their squares is 261, we have the equation ( x^2 + y^2 = 261 ).

We can use the first equation to express one of the variables in terms of the other. For example, we can solve for ( x ) to get ( x = 9 - y ).

Substituting this expression for ( x ) into the second equation, we get ( (9 - y)^2 + y^2 = 261 ).

Expanding and simplifying, we have ( 81 - 18y + y^2 + y^2 = 261 ), which becomes ( 2y^2 - 18y + 81 - 261 = 0 ), and then ( 2y^2 - 18y - 180 = 0 ).

Now, we can use the quadratic formula to solve for ( y ):

[ y = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ]

Where ( a = 2 ), ( b = -18 ), and ( c = -180 ).

Plugging these values into the formula, we get:

[ y = \frac{{-(-18) \pm \sqrt{{(-18)^2 - 4(2)(-180)}}}}{{2(2)}} ] [ y = \frac{{18 \pm \sqrt{{324 + 1440}}}}{{4}} ] [ y = \frac{{18 \pm \sqrt{{1764}}}}{{4}} ] [ y = \frac{{18 \pm 42}}{{4}} ]

This gives us two possible values for ( y ): ( y = \frac{{18 + 42}}{{4}} = 15 ) or ( y = \frac{{18 - 42}}{{4}} = -6 ).

Now, we can use either value of ( y ) to find the corresponding value of ( x ) using the equation ( x = 9 - y ).

If ( y = 15 ), then ( x = 9 - 15 = -6 ). However, this does not satisfy the condition that the sum of the two numbers is 9, so we discard this solution.

If ( y = -6 ), then ( x = 9 - (-6) = 15 ).

Therefore, the two numbers are 15 and -6.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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