Mathematics: By letting y = x^1/3, or otherwise, find the values of x for which x^1/3 -2x^-1/3 = 1

By letting y = x^1/3, or otherwise, find the

Ответ:

jrios4983

12.01.2022

Mathematics

In this case, the problem is asking us to solve the equation

$x^{\frac{1}{3}} - \dfrac{2}{x^{\frac{1}{3}}} = 1$

by substituting $y = x^{\frac{1}{3}}$ .

First, let's substitute the variable into the original equation:

$y - \dfrac{2}{y} = 1$

Now, let's solve:

$y - \dfrac{2}{y} = 1$

Set up

$y\Bigg(y - \dfrac{2}{y}\Bigg) = y(1) \Rightarrow y^2 - 2 = y$

Multiply the entire equation by

to remove the fraction over

y^2 - y - 2 = 0

Subtract

from both sides of the equation for easier factoring

(y - 2)(y + 1) = 0

Factor

$y - 2 = 0 \,\, \textrm{and} \,\, y + 1 = 0$

Solve the factored equation using the Zero Product Property

y = 2, -1

Solve each equation

Now, we aren't done yet. We have to find our answer in terms of the original variable, . To do this, set each value for into the substitution equation we found earlier, $y = x^{\frac{1}{3}}$ :

$2 = x^{\frac{1}{3}}$

2^3 = x

x = 8

$-1 = x^{\frac{1}{3}}$

(-1)^3 = x

x = -1

The solutions for the equation are x = -1, 8.

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Ответ:

jahkin0256

02.04.2020

Mathematics

Step-by-step explanation:

Industries Pollute because of following reasons

Lack of Policies and Unplanned industrial growthApplication of obsolete technologiesInefficient Waste disposal

As the cost of disposal is high so industries dump their waste in the nearby water bodies which causes water pollution. As industries want to maximize their profit so they neglect the disposal part to increase it.

Proper disposal includes the treatment of waste material to reduce its hazardous nature.

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By letting y = x^1/3, or otherwise, find the values of x for which x^1/3 -2x^-1/3 = 1

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