# Solve for t? confused?

(3/4)t^(1/4) - (1/2)t^(3/4) = 0

what is t?

0, 9/4 is wrong or not all answers

Actually it looks like you people are right and the answer key may be wrong, thanks for the help on doing this question everyone

Sorry to have doubted your response! :)

### 4 Answers

- 1 decade agoFavorite Answer
t = {0,9/4}

(3/4)t^(1/4) = (1/2)t^(3/4)

(3/4)^4 * t = (1/2)^4 * t³

t² = (6/4)^4

t = (3/2)²

But note that t = 0 solves the original equation too.

Since you doubt, plug and check.

(3/4) * 0^(1/4) = (1/2) * 0^(3/4) ... Yep.

(3/4) * (9/4)^(1/4) = (1/2) * (9/4)^(3/4)

(81/256) * (9/4) = (1/16) * (729/64)

79/1060 = 729/1060 ... Yep

If you still doubt, plot

y(t) = (3/4)t^(1/4) - (1/2)t^(3/4)

and see how many times it crosses the t axis.

- William BLv 71 decade ago
(3/4)t^(1/4) = (1/2) t^ (3/4)

Take both sides to the 4th power.

81/256 t = 1/16 t^3

Multiple by 16: t^3 - 81/16 t = 0 Factor

t (t + 9/4) ( t - 9/4) = 0 t = 0, 9/4, - 9/4

But -9/4 must be rejected . In the original problem you would be taking the 4th root of a negative number.

- PuzzlingLv 71 decade ago
One solution, by inspection is t = 0.

Let's look for another:

(3/4)t^(1/4) - (1/2)t^(3/4) = 0

Add (1/2)t^(3/4) to both sides:

(3/4)t^(1/4) = (1/2)t^(3/4)

Multiply both sides by 2:

(3/2)t^(1/4) = t^(3/4)

Divide both sides by t^(1/4)* ... note, if t = 0, you can't do this step.

3/2 = t^(3/4) / t^(1/4)

Remember this rule x^a / x^b = x^(a-b):

3/2 = t^(1/2)

3/2 = √t

Square both sides:

9/4 = t

Answer:

t = 0

t = 9/4