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The sum of the squares of two numbers is 225 and the square oftheir sum is 441. What is the reciprocal of their product?​

 Sep 4, 2020
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Lets first denote x and y as the 2 numbers, so this means:

1.x^2+y^2+225

2.(x+y)^2=441

Expanding the second equation we get that x^2+2xy+y^2+441

Subtracting the 2 equation from the 1st one we get 2xy=441-225 2xy=216 and xy=108

The problem asks for the reciprocal of thier product so 1/xy=1/108

And thus 1/108 is our final answer

 Sep 4, 2020

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