Question

Two numbers differ by 7, and the sum of their squares is 29. Find the numbers.

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Rasheed

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72 Answers

let numbers are x and y.
then x-y=7...............(1) and x^2+y^2=29
From (1), \left(x-y\right)^2=49 x^2+y^2-2xy=49
29-2xy=49
xy=-10 then y=-10/x,
Now from (1),
x+\frac{10}{x}=7 x^2-7x+10=0 so x=2,5, then y=-5,-2
So the numbers are 2,-5 or 5,-2

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