# The sum of the numbers is 8 and the sum of their squares is 170. How do you find the numbers?

Mar 5, 2016

$x = 11 , x = 7$

#### Explanation:

It is possible to solve for 2 numbers as two conditions are given.and their sum should be 18 not 8
If one number is taken to be x then the other one is 18-x
By the given condition
${x}^{2} + {\left(18 - x\right)}^{2} = 170$
$\implies 2 {x}^{2} - 36 x + 324 = 170$
Dividing both sides by 2
$\implies {x}^{2} - 18 x + 162 - 85 = 0$
$\implies {x}^{2} - 18 x + 77 = 0$
$\implies {x}^{2} - 11 x - 7 x + 77 = 0$
$\implies x \left(x - 11\right) - 7 \left(x - 11\right) = 0$
$\implies \left(x - 11\right) \left(x - 7\right) = 0$
$x = 11 , x = 7$
So one no is 11 and another is 7

Is the correction OK?
Intimate ,pl