# 02 - Solution to Radical Equations

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

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

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

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

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

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

Solve for $x$ from the following equations

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

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

**Problem 3**

A man bought a cellphone and laptop for P50,000.00, paying three times as much for the laptop as for the cellphone. How much did each cost?

**Problem 4**

Two boys, counting their money, found that together they had P372, and that Rody had ﬁve times as much as Mar. How much had each?

**Problem 1**

The sum of two numbers is 120. If the greater number is four times the less, what are the numbers?

**Problem 2**

The greater of two numbers is twice the less, and the sum of the numbers is 96. What are the numbers?

**Problem**

What is the equation of the curve passing through the point (3, -2) and having a slope at any point (x, y) equal to (x^{2} + y^{2}) / (y^{3} - 2xy)?

Topics in this quiz:

- Present economy
- Simple interest
- Simple Discount
- Compounded interest
- Annuity
- Perpetuity
- Capitalized cost
- Bond

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The problems in this quiz are common optimization problems in engineering lincesure examinations. The allotted time is 30 minutes for you to solve all ten problems. This is to simulate the 100 items board examination given for 5 hours.

All of the problems here can be solved without the aid of differentiation if you know the exact variable relationships for maximum and minimum quantity. Example is, if you are required to inscribed the largest rectangle in a given a circle, differentiation will lead you to a square.

If you already know that it is a square, then you don't need to do the differentiation. Go directly in solving the square for faster solution. All of the problems here can be done in this way, that is, if you know the variable relationship of the situation. If not, then you can still do the differentiation to solve the problem.

The 10 problems you are going to answer are taken from a pool of problems in growing numbers. We are constantly adding problems in here, if you take this quiz again chances are, you will encounter different sets of problems.

Note that you are only given up to 3 times to take this quiz. So fire your best shots and good luck.

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