- Difficulty
- Standard
- Suggested time
- 3 min
- Marks
- 2
Power functions and first sketches practice question 7
Find the positive value of at which the curves below intersect.
Where two curves meet, their -values agree. What do and have in common that you could take out, rather than cancel?
Set and factor out the common power of .
After factoring you get . Only one solution is positive.
An exact expression, or a decimal to three decimal places.
Theory UBC Math 100 §1.1Key results
Worked solution
Strategy
Set the formulas equal and factor out the lowest power of x. The factor that remains, x² − 5, is a quadratic in x whose positive root is the answer.
Working
Everything to one side.
Factor out x², the lowest power present.
Two power functions with positive exponents always meet at the origin; the question wants the positive one.
Answer
The answer is the square root of 5, about 2.236.
Check
At x = √5 both curves are at height 25, since x⁴ = 5² and 5x² = 5 · 5.
Where this goes wrong
Answering x = 5 by cancelling x² on both sides and forgetting the equation that remains is x² = 5, not x = 5.
Try a similar question
The curves and meet at three points. Find the largest -coordinate at which they meet.Saved in this browser only.