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# Help

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The difference between two numbers is 9, and the sum of the squares of each number is 153. What is the value of the product of the two numbers?

Sep 13, 2018

#1
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Sep 13, 2018
edited by Guest  Sep 13, 2018
#2
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When you say " the sum of the squares of each number is 153", I take to mean "the sum of the squares of both numbers is 153". Based on that assumption, then we have:

x - y =9................................(1)

x^2 + y^2 = 153..................(2)

From (1) above: x =9 + y.   sub this into (2) above:

(9 + y)^2 + y^2 = 153, solve for y

y^2 + 18y + 81 + y^2 =153

2y^2 + 18y + 81 - 153 = 0

2y^2 + 18y - 72 = 0 factor:

2(y - 3)(y + 12) = 0   divide both sides by 2

(y - 3)(y+ 12) = 0

y = 3     or    y = -12 and:

x =12    or    x =- 3

x*y =3*12 =36  or -3*-12 =36

Sep 13, 2018
#3
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Here is another method:

Let the numbers be x and y

$$(x-y)^2=x^2-2xy+y^2\\ \text{But we are told that } x-y=9 \text{ and that } x^2+y^2=153\\ so\\ (9)^2=153-2xy\\ 81-153=-2xy\\ -72=-2xy\\ xy=36$$

So the product of the 2 numbers is 36.

Sep 14, 2018