Anonymous

# Solve for t? confused?

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

what is t?

Update:

0, 9/4 is wrong or not all answers

Update 2:

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! :)

Relevance

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.

(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.

t = 9/4

One solution, by inspection is t = 0.

Let's look for another:

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

(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