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The sum of squares of two numbers is 90 and the squares of their diffe

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Bunuel
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The sum of squares of two numbers is 90 and the squares of their diffe [#permalink] New post   29 Jul 2021, 08:30
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If the sum of squares of two numbers is 90 and the square of their difference is 46, what is the product of the two numbers ?

(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
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A
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Bacco361
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Re: The sum of squares of two numbers is 90 and the squares of their diffe [#permalink] New post   29 Jul 2021, 10:03
The sum of two squares is 90: a^2+b^2=90
and the square of their difference is 46: (a-b)^2=46

First equation: a^2=90-b^2
Second equation (FOIL): a^2-2ab+b^2=46

Put first equation in second equation: 90-b^2-2ab+b^2=46
Solve it for ab, which equals 22
IMO A)
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abuc0112
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Re: The sum of squares of two numbers is 90 and the squares of their diffe [#permalink] New post   29 Jul 2021, 10:05
X2 + Y2 = 90 equation 1

(X-Y)2 =46

X2 + Y2 = 2XY +46 equation 2

Combine equations 1 & 2

90 =2XY +46
90-46 =2XY
44=2XY
22 =XY
Ans: A
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Re: The sum of squares of two numbers is 90 and the squares of their diffe [#permalink]
29 Jul 2021, 10:05
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