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Find 2 numbers that sum to 21 and the sum of the squares is 261.
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There are two statements made, which can be written as two equations:
The sum of two numbers are $21: x+y=21$ The sum of the squares is $261: x^{2}+y^{2}=261$
We are asked to find $x$ and $y$.
Since we have the sums of the numbers and the sums of their squares; we can use the square formula of $x+y$, that
is:
$(x+y)^{2}=x^{2}+2 x y+y^{2} \ldots$ Here, we can insert the known values $x+y$ and $x^{2}+y^{2}$
$(21) 2=261+2 x y \ldots$ Arranging to find $x y:$ $441=261+2 x y$
$441-261=2 x y$
$180=2 x y$
$x y=180 / 2$
$x y=90$
We need to find two numbers which multiply to 90 . Checking the answer choices, we see that in (b), 15 and 6 are given, which sum to $90(15 * 6=90)$ and their squares sum to $261(152+62=225+36=261)$.
by Diamond (80,748 points)

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