Question

The sum of the squares of two consecutive multiples of 7 is 673 . Find the multiples

Answer 1

Step-by-step explanation:

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

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