Question

The sum of the squares of two consecutive multiples of 4 is 1360. Find the numbes.

Answer 1

Let the two consecutive multiples of 4 be x , x+4

Gn that

x^2 + (x+4)^2 = 1360

ie x^2+x^2+8x+16=1360

ie
$2x ^{2} + 8x - 1344 = 0$
ie
${x}^{2} + 4 - 672 = 0$
ie
${x}^{2} + 28x - 24x - 672 = 0$
ie
$x(x + 28) - 24(x + 28) = 0$
$(x + 28)(x - 2 4) = 0$
$x = - 28 \: \: (rejected ) \\ x = 24$
Thus the no.s are 24 28