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3 years ago

What are the characteristics of a radical equation?

1 answer:

4 0

<span>What are the characteristics of a radical equation?

Radical equations are those equations where the variable is inside a radical.
For example: √x - 5 = 0 is a radical equation but x -√5 = 0 is not a radical equations.

How is solving radical equations similar to solving linear equations?

You search to isolate the variable, by performing identical operations on both sides of the equation.

Why is it important to check the solutions to a radical equation?

This is important when the index of the root is an even number. For example 2. When you square a square root you force the results to be positive and this may hide the real condition of the original equation.

For example, √x + 5 = 0

=> √x = -5

=>(√x)^2 = (-5)^2

=> x = 25

When you check: √x + 5 =√25 + 5 = 5 + 5 = 10 which is contradictory with the original equation. You have to discard the solution, becasue none real number exists whose square root is negative, which means that √x + 5 = 0 does not have a real solution.

Create your own radical equation. Describe in complete sentences and demonstrate the process in finding its solution(s)

√(3x+1) - 10 = 0

1) isolate the radical: √(3x + 1) = 10

2) Square both sides: [√(3x + 1)]^2 = 10^2

=> 3x + 1 = 100
=> 3x = 99
=> x = 33

3) Check

√[(3(33) + 1] - 10 = √(99 + 1) - 10 = √100 - 10 = 10 - 10 = 0

Then the solution is correct

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Step-by-step explanation:

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Help. Please. Thank You.

GenaCL600 [577]

Answer:

$(A)\ a=-6;b=4\\\\ (B)\ a=6;b=-4$

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+c$

Where "m" is the slope and "c" is the y-intercept.

By definition:

1. If the lines of the System of equations are parallel (whrn they have the same slope), the system has No solutions.

2. If the they are the same exact line, the System of equations has Infinite solutions.

(A) Let's solve for "y" from the first equation:

$3x-2y=-1\\\\-2y=-3x-1\\\\y=\frac{3}{2}x+\frac{1}{2}$

You can notice that:

$m=\frac{3}{2}\\\\c=\frac{1}{2}$

In order make that the System has No solutions, the slopes must be the same, but the y-intercept must not. Then, the values of "a" and "b" can be:

$a=-6\\\\b=4$

Substituting those values into the second equation and solving for "y", you get:

$-6x+4y=-2\\\\4y=6x-2\\\\y=\frac{6}{4}x-{2}{4}\\\\y=\frac{3}{2}x-\frac{1}{2}$

You can idenfity that:

$m=\frac{3}{2}\\\\c=-\frac{1}{2}$

Therefore, they are parallel.

(B) In order make that the System has Infinite solutions, the slopes and the y-intercepts of both equations must be the same. Then, the values of "a" and "b" can be:

$a=6\\\\b=-4$

If you substitute those values into the second equation and then you solve for "y", you get:

$6x+(-4y)=-2\\\\-4y=-6x-2\\\\y=\frac{-6}{-4}x-\frac{2}{-4}\\\\y=\frac{3}{2}x+\frac{1}{2}$

You can identify that:

$m=\frac{3}{2}\\\\b=\frac{1}{2}$

Therefore, they are the same line.

3 0

3 years ago