SOLUTION: suppose that q is a rational number that is not 0 or 1, and that x is irrational and nonzero. prove that cubic root ((q^2-1)/(qx)) is irrational.
please prove by contradiction (
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-> SOLUTION: suppose that q is a rational number that is not 0 or 1, and that x is irrational and nonzero. prove that cubic root ((q^2-1)/(qx)) is irrational.
please prove by contradiction (
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Question 1135667: suppose that q is a rational number that is not 0 or 1, and that x is irrational and nonzero. prove that cubic root ((q^2-1)/(qx)) is irrational.
please prove by contradiction (assuming cubic root ((q^2-1)/(qx)) is rational.)
thanks for helping Answer by ikleyn(52858) (Show Source):
Let's assume that is a rational number R:
= R,, where R is a rational number.
Then x = , and it is rational number, since the numerator and denominator are rational numbers
(partly according to the condition and partly according to the assumption).
But we are given that x is irrational - CONTRADICTION.
The contradiction proves that our assumption is FALSE.
