Question

if 20 is subtracted from 16 times of a number, the resulting number is three times the square of the number. find the number

Answer 1

Answer:

2

Step-by-step explanation:

Let the number be 'x'

According to the question,

16x - 20 = 3 * x²

⇒ 3x² - 16x + 20 = 0   ...(i)

Now, let us factorise the above equaion.

3 * 20 = 60

The factors of 60 are (1 , 60) , ( 2 , 30) , ( 3 , 10) , (4 , 20) , (5 , 12), (6 , 10).

The sum of 6 and 10 is 60.

So the equation (i) can be written as,

3x² - 6x - 10x + 20 = 0

⇒ 3x (x - 2) - 10 (x - 2) = 0

⇒(3x - 2) (x - 2 ) = 0

Either 3x -2 = 0 or x - 2 = 0

Either x = 3/2 or x = 2

But x = 3/2 does not satisfy equation (i). So x = 2