the sum of two numbers is 18.The sum of their squares is at most 170.Find all pairs of numbers that satisfy these conditions.​

Sagot :

Let x and y be the 2 numbers were looking for.

In the given , we know that

x+y = 18

x^2 + y^2 = 170

First we have to find something to substitute to either x and y to make one variable solvable

lets use x to sub

x= 18 - y

(18 - y)^2 + y^2 = 170

324 - 36y + y^2 + y^2 = 170

162 - 18y + y^2 = 85

y^2 - 18y + 77 = 0

(y - 11)(y - 7) = 0

y = 11

y = 7

then look for values of x with the value you got on y

x + 11 = 18

x= 7

x+ 7 = 18

x= 11 (Just the same as y)

so the answers will be 7 and 11