Question

the sum of the squares of two consecutive multiples of 7 is 637. Find the multiples​

Answer 1

Step-by-step explanation:

let one number be x and 2nd be x +7

(here x is a multiple of 7 )

According to question

${x}^{2} + {(x + 7)}^{2} = 637 \\ {x}^{2} + {x}^{2} + 14x + 49 - 637 = 0 \\ 2 {x}^{2} + 14x - 588 = 0 \\ 2( {x}^{2} + 7x - 294) = 0 \\ {x}^{2} + 21x - 14x - 294 = 0 \\ x(x + 21) - 14( + 21) = 0 \\ (x - 14)(x + 21) = 0 \\ x - 14 = 0 \\ x = 14$

therefore one number is 14 and another is 21 .