# substitution

## 02 - Solution to Radical Equations

Determine the value of $x$ from the following equations:

- $\sqrt{(4 - x^2)^3} + 3x^2\sqrt{4 - x^2} = 0$

- $\dfrac{1}{3x - 2} - \dfrac{8}{\sqrt{3x - 2}} = 9$

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## 01 - Solution to Radical Equations

Solve for $x$ from the following equations

- $\sqrt{3 - x} + \sqrt{4 - 2x} = \sqrt{3 - 3x}$

- $\sqrt{\dfrac{2x + 4}{x - 5}} + 8\sqrt{\dfrac{x - 5}{2x + 4}} = 6$

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## Problem 05 | Substitution Suggested by the Equation

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## Problem 03 | Substitution Suggested by the Equation

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## Problem 02 | Substitution Suggested by the Equation

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## Problem 01 | Substitution Suggested by the Equation

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## Substitution Suggested by the Equation | Bernoulli's Equation

**Substitution Suggested by the Equation**

Example 1

The quantity (2x - y) appears twice in the equation. Let

$z = 2x - y$

$dz = 2~dx - dy$

$dy = 2~dx - dz$

Substitute,

$(z + 1)~dx - 3z(2~dx - dz) = 0$

then continue solving.

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## Problem 04 | Equations with Homogeneous Coefficients

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## Problem 03 | Equations with Homogeneous Coefficients

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## Problem 02 | Equations with Homogeneous Coefficients

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