Question

The sum of squares of two consecutive multiples of 2 is 637.Find the multiples

Answer 1

solution:-

let the number multiple of. 7 = 7x
then
consecutive multiples of 7 = 7(x+1)

now
according to question
(7x)² + {7 (x+1)}² = 637
= 49 x² + 49 (x+1)² = 637
= 49 x² + 49( x² +1+2x)
= 98x² +98 x +49 = 637
= 98x² +98x = 637-49 = 588
=> x² +x= 6. or = x² + x -6 =0

=> x² +3x -2 x -6 = 0
=> x(x+3) -2 (x+3) = 0
=> x-2 =0. and x+3 = 0
=> x= 2 and -3 answer

hence
(1) if x = 2
the number multiple of 7 is 7×2 =14
it's consecutive number multiple of 7 is = 7×(2+1) = 7×3 = 21

(2) if x =-3
the number multiple of 7 is 7×(-3) = -21
it's consecutive number multiple of 7 is = 7×(-3 +1) = 7× (-2) = -14