What is x^3-4x^2+2<x^3-2x^2+1 ?

The solution to x^3-4x^2+2 sqrt(1/2)

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x^3-4x^2+2<x^3-2x^2+1

x^{3} - 4 x^{2} + 2 < x^{3} - 2 x^{2} + 1

x < - \frac{1}{2} or x > \frac{1}{2}

Interval Notation

(- \infty, - \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Decimal Notation

x < - 0.70710 \dots or x > 0.70710 \dots

Solution steps

x^{3} - 4 x^{2} + 2 < x^{3} - 2 x^{2} + 1

Rewrite in standard form

- 2 x^{2} + 1 < 0

Move

1

to the right side

- 2 x^{2} < - 1

Multiply both sides by

- 1

2 x^{2} > 1

Divide both sides by

2

x^{2} > \frac{1}{2}

For

u^{n} > a

, if

n

is even then

x < - \frac{1}{2} or x > \frac{1}{2}

\frac{- 3}{- x + 7} > 0

\frac{1}{( x - 1 )} \leq 2

3 x^{3} \geq 12

\frac{( x ^{2} - 19 x + 88 )}{( x ^{2} - 11 x + 24 )} \leq 0

\frac{2}{m - 1} \geq 1

What is x^3-4x^2+2<x^3-2x^2+1 ?
The solution to x^3-4x^2+2<x^3-2x^2+1 is x<-sqrt(1/2)\lor x>sqrt(1/2)