Question

Find two consecutive positive even integers whose product is 224

Answer 1

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Answer 2

14 and 16 are the two consecutive positive even integers whose product is 224

Solution:

Let the consecutive positive even integer be x and x + 2

Product is 224

Therefore,

$x(x+2) = 224\\\\x^2 + 2x - 224 = 0$

$Split\ the\ middle\ term\\\\x^2 -14x +16x-224 = 0\\\\\mathrm{Break\:the\:expression\:into\:groups}\\\\\left(x^2-14x\right)+\left(16x-224\right) = 0\\\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2-14x\mathrm{:\quad }x\left(x-14\right)\\\\\mathrm{Factor\:out\:}16\mathrm{\:from\:}16x-224\mathrm{:\quad }16\left(x-14\right)\\\\x\left(x-14\right)+16\left(x-14\right) = 0\\\\\mathrm{Factor\:out\:common\:term\:}x-14\\\\\left(x-14\right)\left(x+16\right) = 0\\\\x = 14\\\\x = -16$

Ignore negative value

Thus,

x = 14

x + 2 = 14 + 2 = 16

Thus 14 and 16 are the two consecutive positive even integers whose product is 224

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