Finding real roots

[Shaw1418]

Hello. I feel so stupid. I'm trying to refresh on Algebra I had a very long time ago. I'm using an algebra II book I bought at a store for teachers and it has very few if any examples. I looked in the back of the book for the answer after trying it. The problem is 7(x - 15)^3/5 = 2401 and the solution is x = 16,807. I don't understand how they get that. Other problems similar to that had 1/2 instead of 3/5 and I understood that. For instance I had another problem like 8(4x + 3) ^1/2 = 49. The solution for that was to divide both sides by 8 first to get 4x + 3 = 6561, then 4x + 3 - 3 = 6561(this was the result of 648/8 = 81 * 81) then 4x/4 = 6558/4. I thought maybe I somehow do the similar to get x = 16,807 on the first mentioned problem but if I multiply 343 * 3/5 I get 205.8, if I multiply 343 * 343 * 343 I get 4,0353,607. If I multiply 343 by itself 5 times I get an astronomical number. So how is 16,807 the answer?

 

[Deleted member 4993]

Hello. I feel so stupid. I'm trying to refresh on Algebra I had a very long time ago. I'm using an algebra II book I bought at a store for teachers and it has very few if any examples. I looked in the back of the book for the answer after trying it. The problem is 7(x - 15)^3/5 = 2401 and the solution is x = 16,807. I don't understand how they get that. Other problems similar to that had 1/2 instead of 3/5 and I understood that. For instance I had another problem like 8(4x + 3) ^1/2 = 49. The solution for that was to divide both sides by 8 first to get 4x + 3 = 6561, then 4x + 3 - 3 = 6561(this was the result of 648/8 = 81 * 81) then 4x/4 = 6558/4. I thought maybe I somehow do the similar to get x = 16,807 on the first mentioned problem but if I multiply 343 * 3/5 I get 205.8, if I multiply 343 * 343 * 343 I get 4,0353,607. If I multiply 343 by itself 5 times I get an astronomical number. So how is 16,807 the answer?

I assume the problem is:

Solve for 'x' while

\(\displaystyle \displaystyle{7 * (x - 15)^{\frac{3}{5}} \ = \ 2401}\)

if it is then first divide by 7 both sides to get:

\(\displaystyle \displaystyle{(x - 15)^{\frac{3}{5}} \ = \ 343}\)

continue......

 

[Deleted member 4993]

I assume the problem is:

Solve for 'x' while

\(\displaystyle \displaystyle{7 * (x - 15)^{\frac{3}{5}} \ = \ 2401}\)

if it is then first divide by 7 both sides to get:

\(\displaystyle \displaystyle{(x - 15)^{\frac{3}{5}} \ = \ 343}\)

continue......

Continuing

\(\displaystyle \displaystyle{(x - 15)^{\frac{1}{5}} \ = \ (343)^{\frac{1}{3}}}\)

\(\displaystyle \displaystyle{(x - 15)^{\frac{1}{5}} \ = \ 7}\)

 

[HallsofIvy]

For instance I had another problem like 8(4x + 3) ^1/2 = 49. The solution for that was to divide both sides by 8 first to get 4x + 3 = 6561, then 4x + 3 - 3 = 6561(this was the result of 648/8 = 81 * 81) then 4x/4 = 6558/4.

This makes no sense at all! Dividing both sides of 8(4x+ 3)^1/2= 49 gives (4x+ 3)^1/2= 49/8= 6.1250, not "4x+ 3= 6561". And squaring both sides, to get rid of the 1/2 power, gives 4x+ 3= 37.515625.