If the sum of the squares of two consecutive positive multiples of 4 is 656, then what is the mean - Maths - Quadratic Equations

Question

If the sum of the squares of two consecutive positive multiples of
4 is 656, then what is the mean of the two multiples?

Neha Sethi · Accepted Answer

Dear student
Let the first multiple =xSo, second multiple=x+4A
T
Qx2+x+42=656⇒x2+x2+16+8x=656⇒2x2+8x-640=0⇒x2+4x-320=0⇒x2-16x+20x-320=0⇒xx-16+20x-16=0⇒x+20x-16=0⇒x+20=0 or x-16=0⇒x=-20 or x=16Since multiple cannot be negative So, x=16So, second multiple =x+4=16+4=20So, the multiples are 16 and 20So, the mean of multiples=16+202=362=18
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If the sum of the squares of two consecutive positive multiples of 4 is 656, then what is the mean of the two multiples?