How Do You Solve (16-x²)³/2 = 40 for x?

  • Thread starter angel
  • Start date
In summary, the conversation discusses solving the equation (16-x^2)^3/2 = 40 by simplifying it to sqrt(16-x^2)^3) = 40 and then taking the cube root of both sides or raising both sides to the power of 2/3. The conversation also notes that the initial step of taking the square root was not necessary.
  • #1
angel
18
0
hi,
im trying to solve this for x:

(16-x^2)^3/2 = 40

ive simplified it by taking the square root, so i get:

sqrt(16-x^2)^3) = 40

now i square both sides and i get:

(16-x^2)^3 = 1600 (Not sure if this is right)

im not sure what to do next. i think i can take the cube root of both sides, but I am not sure.
Can someone please help me.
thanks
 
Physics news on Phys.org
  • #2
Yes, you take the cube root of both sides. In fact, you could've just raised both sides to the power of 1/(3/2) = 2/3 in the first place, to get 16 - x^2 = 40^(2/3) (which should be easy to solve).
 
  • #3
By the way, you didn't actually "take the square root" at the beginning: you simply rewrote the "1/2" power as a square root. You could have said "square both sides" initially.
 

What does the equation (16-x^2)^3/2 = 40 mean?

This equation is asking you to find the value of x that makes the expression (16-x^2) raised to the power of 3/2 equal to 40.

What are the steps to solve this equation?

The steps to solve this equation are:
1. Simplify the exponent on the left side of the equation by distributing the power.
2. Subtract 40 from both sides of the equation.
3. Simplify the left side of the equation again by expanding the binomial.
4. Isolate the term with x by dividing both sides by 16.
5. Take the square root of both sides of the equation.
6. Solve for x by taking both the positive and negative square roots.

What is the solution to this equation?

The solutions to this equation are x = 2 and x = -2.

How can I check my solution?

You can check your solution by plugging in the values of x into the original equation and seeing if it simplifies to 40.

What is the significance of the solutions to this equation?

The solutions to this equation represent the values of x that satisfy the original equation and make the expression (16-x^2) raised to the power of 3/2 equal to 40. These solutions may have practical applications in areas such as physics, engineering, and economics.

Similar threads

MHB [ASK] Minimum Surface Area
    • Calculus
Replies
4
Views
958
B Trigonometric substitution, a case I'd like to share
    • Calculus
Replies
3
Views
1K
I A simple equation with simple solution - how to solve it?
    • Calculus
Replies
12
Views
1K
Solve ##\sqrt{\dfrac{x}{y}}+\sqrt{\dfrac{y}{x}}=4\dfrac{1}{4} \cdots##
    • Precalculus Mathematics Homework Help
Replies
10
Views
302
MHB Approximating the value of a function
    • Calculus
Replies
1
Views
1K
MHB How to solve for x using 2nd derivative?
    • Calculus
Replies
8
Views
954
MHB Finding the Derivative of the Inverse Function of a Cubic Polynomial
    • Calculus
Replies
5
Views
2K
A Non solvable integral? (dx/dt)^2 dt
    • Calculus
Replies
3
Views
2K
I How Do You Integrate 1/√(x^3 + x^2 + x + 1) dx?
    • Calculus
Replies
8
Views
1K
B What went wrong with (-x)^2=x^2?
    • General Math
Replies
22
Views
555

Hot Threads

Recent Insights

Back
Top