Question

If two numbers differ by 2 and their product is 360, then
find the numbers.
​

Answer 1

Solution :-

Given : Two numbers differ by 2.

Let us assume that one number be x.

So, other number = x - 2

According to the question,

=> x(x - 2) = 360

=> x² - 2x - 360 = 0

=> x² - 20x + 18x - 360 = 0

=> x(x - 20) + 18(x - 20) = 0

=> (x + 18) (x - 20) = 0

=> x = - 18 or x = 20

Substituting the both value of x to get the other number :

= - 18 - 2 = - 20

or, 20 - 2 = 18

Answer : The numbers are - 18 and - 20 or 20 and 18.

Answer 2

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According to the given question:-

• 2 numbers differ by 2

• Let y be one number

• Let Other number = y - 2

So,

➡$x(x - 2) = 360$

➡x² - 2x - 360 = 0

➡x² - 20x + 18x - 360 = 0

➡$x(x - 20) + 18(x - 20) = 0$

➡$(x + 18) (x - 20) = 0$

➡$x = - 18\: or\: x = 20$

Adding the both value of x tothe other number:-

➡$= - 18 - 2 = - 20$

➡$or \:also\: can\: be\: (20 - 2 = 18)$