Question 297091: 16r^3-9r=0 solve please. thank you so much
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 16r^3 - 9r = 0
Factor out the r on the left side of the equation to get
r * (16r^2 - 9) = 0
r = 0 will satisfy this equation because anything times 0 equals 0.
16r^2 - 9 = 0 will also satisfy this equation because anything times 0 equals 0.
Solve for 16r^2 - 9 = 0
Add 9 to both sides of this equation to get 16r^2 = 9
Divide both sides of this equation by 16 to get r^2 = (9/16)
Take the square root of both sides of this equation to get r = +/- sqrt(9/16)
Since sqrt(9/16) is the same as sqrt(9) / sqrt(16), and since sqrt(9) = 3, and since sqrt(16) = 4, you get r = +/- 3/4
You have 3 possible answers to this equation.
They are:
r = 0
r = 3/4
r = -3/4
Plug those values into the original equation to see if they hold up.
Your original equation is 16r^3 - 9r = 0
When r = 0, this equation becomes 0 - 0 = 0 which is true.
When r = 3/4, this equation becomes 16*27/64 - 9*3/4 = 432/64 - 27/4 = 6.75 - 6.75 = 0 which is true.
When r = -3/4, this equation becomes 16*-27/64 + 9*3/4 = -432/64 + 27/4 = -6.75 + 6.75 = 0 which is true.
All 3 answers are solutions to the original equation.
|
|
|
