The sum of the squares of the two consecutive multiples of 7 is 637, find the multiples?
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Step-by-step explanation:
let the numbers be x and x + 7
x² + (x+7)² = 637
=> x² + x² + 49 + 14x = 637
=> 2x² + 14x + 49 - 637 = 0
=> 2x² + 14x - 588 = 0
=> x² + 7x - 294 = 0
=> x² +21x - 14x - 294 = 0
=> x(x+21) - 14(x + 21) = 0
=> (x+21)(x - 14) = 0
=> x + 21 = 0 => x = -21
=> x - 14 = 0 => x = 14
therefore numbers are 14 and 21 or -21 and -14
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