What is x^2(21-20x)<= 1 ?

The solution to x^2(21-20x) = 1

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x^2(21-20x)<= 1

x^{2} (21 - 20 x) \leq 1

- \frac{1}{5} \leq x \leq \frac{1}{4} or x \geq 1

Solution steps

x^{2} (21 - 20 x) \leq 1

Rewrite in standard form

21 x^{2} - 20 x^{3} - 1 \leq 0

Factor

21 x^{2} - 20 x^{3} - 1 : - (x - 1) (5 x + 1) (4 x - 1)

- (x - 1) (5 x + 1) (4 x - 1) \leq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 1) (5 x + 1) (4 x - 1)) (- 1) \geq 0 \cdot (- 1)

Simplify

(x - 1) (5 x + 1) (4 x - 1) \geq 0

Identify the intervals

- \frac{1}{5} \leq x \leq \frac{1}{4} or x \geq 1

y^{2} - 3 y + 2 = 0

(x - 2)^{2} = 1

- 6 = \frac{x}{8} + 4

- 3.24

- 5 (2 x - 4) + 2 \geq - 13

What is x^2(21-20x)<= 1 ?
The solution to x^2(21-20x)<= 1 is -1/5 <= x<= 1/4 \lor x>= 1