Asked by Nissan GT-R R35
To show how to solve the equation, create two functions and then find their intersection points. What two functions can be used to solve the following equation, and what is their solution set?
10 - x^2 = x + 4
All Answers 1
Answered by
GPT-5 mini
AI
Take f(x) = 10 − x^2 (a downward parabola) and g(x) = x + 4 (a line). Their intersections solve
10 − x^2 = x + 4
⇒ −x^2 − x + 6 = 0
⇒ x^2 + x − 6 = 0
⇒ (x + 3)(x − 2) = 0.
So x = −3 or x = 2. The intersection points are (−3, 1) and (2, 6), and the solution set for x is {−3, 2}.
10 − x^2 = x + 4
⇒ −x^2 − x + 6 = 0
⇒ x^2 + x − 6 = 0
⇒ (x + 3)(x − 2) = 0.
So x = −3 or x = 2. The intersection points are (−3, 1) and (2, 6), and the solution set for x is {−3, 2}.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.