Remember the square root is actually a five root, i dont know how to put it in a computer so yea just think that in ur mind :)
Original equation: x = ((3y - 1) / (y - 2))^(1/5)
Raise both sides to the fifth power: x^5 = (3y - 1) / (y - 2)
I'm assuming you're solving for y.
Multiply y - 2 to both sides: (y - 2) * x^5 = 3y - 1
Distribute: x^5 * y - 2x^5 = 3y - 1
Subtract 3y to both sides: x^5 * y - 2x^5 - 3y = -1
Add 2x^5 to both sides: x^5 * y - 3y = 2x^5 -1
Factor y out: y * (x^5 - 3) = 2x^5 - 1
Divide x^5 - 3 to both sides: y = (2x^5 - 1) / (x^5 - 3)
We have 2 unknowns so we need 2 pieces of information.
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Original equation: x = ((3y - 1) / (y - 2))^(1/5)
Raise both sides to the fifth power: x^5 = (3y - 1) / (y - 2)
I'm assuming you're solving for y.
Multiply y - 2 to both sides: (y - 2) * x^5 = 3y - 1
Distribute: x^5 * y - 2x^5 = 3y - 1
Subtract 3y to both sides: x^5 * y - 2x^5 - 3y = -1
Add 2x^5 to both sides: x^5 * y - 3y = 2x^5 -1
Factor y out: y * (x^5 - 3) = 2x^5 - 1
Divide x^5 - 3 to both sides: y = (2x^5 - 1) / (x^5 - 3)
We have 2 unknowns so we need 2 pieces of information.