Question

Find the real numbers whose sum is 8 and whose product is 16​

Answer 1

The number is 4.

Explanation:

First, you have to form equations for the numbers. Let x be the first number and y be the second :

`x + y = 8`

`xy = 16`

Next, you have to solve the simultaneous equation by substitution method :

`x + y = 8 - - - (1)`

`xy = 16`

`y = (16)/(x) - - - (2)`

`(2)⇒(1)`

`x + (16)/(x) = 8`

`\frac{ {x}^(2) + 16 }{x} = 8`

`{x}^(2) + 16 = 8x`

`{x}^(2) - 8x + 16 = 0`

`{(x - 4)}^(2) = 0`

`x = 4`

`substitute \: x = 4 \: into \: (1)`

`4 + y = 8`

`y = 4`