Question 825600: The sum of two numbers is 24. The sum of the squares of the two numbers is 306. What is the product of the two numbers?
Found 2 solutions by TimothyLamb, rothauserc:
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! --
x + y = 24
xx + yy = 306
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y = 24 - x
xx + (24 - x)(24 - x) = 306
xx + 576 - 48x + xx = 306
2xx - 48x + 576 - 306 = 0
2xx - 48x + 270 = 0
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the above quadratic equation is in standard form, with a=2, b=-48, and c=270
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
2 -48 270
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
x = 15
x = 9
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answer:
15*9 = 135
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Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! x + y = 24
x^2 +y^2 = 306
solve for x in the first equation
(24-y)^2 +y^2 = 306
576 -48y +y^2 +y^2 = 306
2y^2 -48y +576 = 306
divide both sides of = by 2
y^2 -24y +288 = 153
y^2 -24y +135 = 0
factor this equation
(y-15) * (y-9) = 0
there are two solutions, (x=9, y=15) and (x=15,y-9)
we are asked for the product of the two numbers
9 * 15 = 15 * 9 = 135
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