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

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

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Answer 1 · 2016-03-05T10:59:56

$x = 11, x = 7$ $x=11,x=7$

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
$x^{2} + {(18 - x)}^{2} = 170$ $x^2+(18-x)^2=170$
$\Rightarrow 2 x^{2} - 36 x + 324 = 170$ $=>2x^2-36x+324=170$
Dividing both sides by 2
$\Rightarrow x^{2} - 18 x + 162 - 85 = 0$ $=>x^2-18x+162-85=0$
$\Rightarrow x^{2} - 18 x + 77 = 0$ $=>x^2-18x+77=0$
$\Rightarrow x^{2} - 11 x - 7 x + 77 = 0$ $=>x^2-11x-7x+77=0$
$\Rightarrow x (x - 11) - 7 (x - 11) = 0$ $=>x(x-11)-7(x-11)=0$
$\Rightarrow (x - 11) (x - 7) = 0$ $=>(x-11)(x-7)=0$
$x = 11, x = 7$ $x=11,x=7$
So one no is 11 and another is 7

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

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