Question

the sum of squares of two consecutive positive integers is 145 find the integers ​

Answer 1

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Answer 2

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

Let the numbers be N and N + 1

Now we have N^2 + (N +1)^2 = 145

=> N^2 + N^2 + 2N + 1 = 145

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

=> N^2 + N - 72 = 0

=> N^2 + 9N - 8N - 72 = 0

=> N(N + 9) - 8(N + 9) = 0

=> (N - 8)(N + 9) = 0

N can be 8 or -9

So the two numbers are (8 , 9) or ( -8 , -9).