Question

The sum of the squares of the two consecutive multiples of 7 is 637, find the multipl​

Answer 1

we have given that

sum of the squares of two consecutive

multiples of 7 is 637.

we have to find

the numbers are????

answer:

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 + 98x + 49 = 637

= 98x² +98x = 637-49 = 588

=> x² + x = 6. or = x² + x -6 = 0

=> x² + 3x -2x -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

⭐⭐hope it will help you⭐⭐