Question

1. What is extraneous solutions?

2. What does the numerator of a fractional exponent mean?
3. What is the complex number?

Answer 1

see explanation

Explanation:

1

An extraneous solution tend to occur when dealing with equations involving radicals or absolute value functions.

Solutions are obtained by solving the equation and then must be verified by substituting them into the original equation.

Although a simplified solution is obtained it may not satisfy the original equation and is therefor extraneous.

2

It is the power that the value is being raised to

For example

rule of exponents

`a^{(m)/(n) }` ⇔
`\sqrt[m]{a^(n) }`

3

A complex number does not appear on the set of real numbers.

It is composed of a real part and an imaginary part, usually in the form

z = a + bi ( where a and b are real )

a is the real part and bi the imaginary part

They are based on
`√(-1)` = i

We can then solve problems involving negative radicals, particularly in solving quadratic equations

x = ±
`√(-16)` = ±
`√(16(-1))` = ±
`√(16)` ×
`√(-1)` = ± 4i

Answer 2

When you multiply through by the LCD and solve the resulting quadratic equation, you get solutions x=2 and x=1. However when we try to check the solution x=2, it causes the first and last denominators to become 0, which is undefined. However x=1 checks.

Explanation: