Question

The sum of the squares of two consecutive multiples of 7 is 1225. find the multiples.

Answer 1

let the first multiple is 7*k and next multiple is 7*(k+1)
therefore
49*k^2 + 49*(k^2 + 2*k + 1) = 1225
49*(2*k^2 + 2*k + 1) = 1225
2*k^2 + 2*k + 1 = 25
k^2 + k -12 =0
k = 3 or -4(rejected)
k=3
k+1 =4
therefore 21 and 28

Answer 2

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