The sum of two positive numbers is 17?

Question

The sum of two positive numbers is 17. While the sum of one of the numbers plus twice the square of the other number is 108.Find the two numbers?

Answer 1

If one number is x, the other is 17 - x.

So (17 - x ) + 2x^2 = 108

2x^2 + 17 - x = 108

subtract 108 from both sides

2x^2 - x - 91 = 0

(2x + 13)(x - 7) = 0

so x = 7 making the other be 10

Answer 2

7 and 10

2 x 49=98

98 + 10 = 108

7 + 10 = 17

how to work it out -

half of 108 is 54 (so you know the square or the 1st number has to be less than 54)

7 is the highest one (49) and common sense will tell you this is the best one to try as the other number has to add to it to get 108 AND 17. Trial and Error shows you it works.

Answer 3

x + y = 17

x + 2y^2 = 108

subtract the first equation from the second the x's cancel out

2y^2 - y = 91

2y^2 - y - 91 = 0

(y-7)(2y+13) = 0

y-7=0  and 2y+13=0

y=7 and y=-13/2 since the numbers must be positive

y=7

x+y=17

x+7=17

x=10

therfore your two numbers are 7 and 10