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The sum of square of two …

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The sum of square of two consecutive multiples of 7 is 637. Find the multiple.

Posted by Arpit Jindal 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Gouri Krishnan 6 years, 10 months ago

(7x) square +(7(x+1)) square= 637
49x^2 + 49(x+1)^2 =637
Taking 49 common
49( x^2 + x^2 +2x +1) = 637
2x^2 + 2x +1 = 637 / 49
= 13
2x^2 + 2x = 13 - 1
= 12
x^2 + x = 6
x (x + 1) =6
2 *3 6
So multiple s are 7x ie 7*2=14
And 21

Avinash Saigal 6 years, 10 months ago

we have given that sum of the squares of two consecutive multiples of 7 is 637. we have to find the numbers are ?? 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 Thank you??

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