What is (x-3x^2)^2<(1-3x)^2 ?

The solution to (x-3x^2)^2<(1-3x)^2 is -1<x< 1/3 \lor 1/3 <x<1

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(x-3x^2)^2<(1-3x)^2

(x - 3 x^{2})^{2} < (1 - 3 x)^{2}

- 1 < x < \frac{1}{3} or \frac{1}{3} < x < 1

Solution steps

(x - 3 x^{2})^{2} < (1 - 3 x)^{2}

Rewrite in standard form

9 x^{4} - 6 x^{3} - 8 x^{2} + 6 x - 1 < 0

Factor

9 x^{4} - 6 x^{3} - 8 x^{2} + 6 x - 1 : (x + 1) (x - 1) (3 x - 1)^{2}

(x + 1) (x - 1) (3 x - 1)^{2} < 0

Identify the intervals

- 1 < x < \frac{1}{3} or \frac{1}{3} < x < 1

\frac{2 x + 3}{15 - 5 x} \geq 0

- 5 u^{2} + 13 u - 6

\frac{x ^{3} y ^{4} x ^{- 2} y ^{- 5}}{y ^{3} x ^{5} y ^{- 2}}

5 (x^{2} - 1) > 24 x

- 33 > 6 a + 3

What is (x-3x^2)^2<(1-3x)^2 ?
The solution to (x-3x^2)^2<(1-3x)^2 is -1<x< 1/3 \lor 1/3 <x<1