The sum of the squares of two consecutive numbers is 145. Find the numbers.

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Let one of the numbers be x.

Then the next consecutive number is (x+1)

Given that the sum of the squares is 145.

==> x^2 + (x+1)^2 = 145

==> x^2 + x^2 + 2x + 1 = 145

==> 2x^2 + 2x - 144 = 0

Now let us divide by 2.

==> x^2 + x - 72...

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