Sum Of Two Numbers Is 20, And Sum Of The Their Squares Is 218. Can You Find The Numbers?

Write this out as you read it;  We'll call one of the numbers N and the other M;

N + M = 20

N²+ M²= 218

Now we have two equations, two unknowns.  We should be able to solve this.

If N + M = 20,  then M = 20 - N

Substitute M into the second equation

N² + (20 - N)² = 218

now solve for N.  begin by expanding the binomial;

N² + 400 - 40N + N² = 218

Then collect terms to simplify

2N² -40N + 182 = 0

we can divide all the way through by 2

N² -20N + 91 = 0

Let's just plug this into the quadratic formula and solve.

-B +/- sqrt(B² - 4AC)
______

In this case, A = 1, B = -20, C = 91

20 +/- sqrt(400 - 4 * 91)
______



20 +/- 6

______

 
the roots are 13, and 7. 

7 + 13 = 20 is true, so far, so good.

7² + 13² = 218

49 + 169 = 218 is true as well,

so those are both of the numbers.

13 and 7 049
169
218
11

Numbers are 12 and 8