The sum of two numbers is 210. If one number is the square of the other, find the set of numbers.
Thanks
x^2+x-210=0
(x-14)(x+15) = 0
Thanks Steve.
One number x.
So, the other number: 210 – x.
According to the given condition,
x^2 = 210 – x,
ox^2 + x – 210 = 0,
or (x + 15) (x – 14) = 0,
or x = –15 or 14.
Therefore, one number is either –15 or 14 and the other number is either (210 + 15) = 225 or (210 – 14) = 196.
To find the set of numbers, we can set up a system of equations based on the given information.
Let's assume that the smaller number is "x" and the larger number is its square, "x^2".
According to the problem, the sum of the two numbers is 210. So, we can write the equation as:
x + x^2 = 210
Next, we can rearrange the equation to get it in quadratic form:
x^2 + x - 210 = 0
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use factoring:
Factor the quadratic equation:
(x + 15)(x - 14) = 0
From here, we have two possible solutions:
1) Set x + 15 = 0: x = -15
In this case, the larger number x^2 would be (-15)^2 = 225.
2) Set x - 14 = 0: x = 14
In this case, the larger number x^2 would be (14)^2 = 196.
Therefore, the set of numbers that satisfy the given conditions is (-15, 225) and (14, 196).