Question

The product of a number and 2 more than that is 168, what are the numbers?

Answer 1

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Let the one number be x and the other number be ( x + 2 ) .

Product of these numbers = 168

$\sf\Longrightarrow x(x+2) = 168 \\\\\Longrightarrow x^2+2x = 168 \\\\\Longrightarrow x^2+2x+1^2= 168 + 1^2 \ \ \ \ \ \ ( Square \ completion \ method )\\\\\Longrightarrow (x+1)^2 = 169 \\\\\Longrightarrow x+1 = \pm 13 \\\\If \ x+1 = +13 \ ,\bf { \ x = 12} \\\\\sf If \ x+1 = -13 \ , \bf \ x = -14$

The numbers are 12 and 14 or -12 and -14 .

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Answer 2

Numbers = 12,14 or -12 , -14

Step-by-step explanation:

Let one number be x. Then,

X(x+2)= 168

x2 + 2x = 168

x2+2x+1= 168 + 1

(x+1)2 = 169

x+1 = Square root of 169

x+1 = 13 or x+1 = - 13

x = 13- 1 = 12 or -13-1 = -14

So,

Numbers are 12,14 or -12 ,-14