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Radical Functions and Equations
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Slide 1

Radical

Radical

Equations

Slide 2

How Do We Solve Radical Equations?

How Do We Solve Radical Equations?

Do Now: Simplify the given expression.

1. 2.

Slide 3

Radical Equations

Radical Equations

An equation in which a variable occurs in the radicand

is called a radical equation. It should be noted, that

when solving a radical equation algebraically,

extraneous roots may be introduced when both sides of

an equation are squared. Therefore, you must check

your solutions for a radical equation.

Solve: √ x - 3 - 3 = 0

√ x - 3 = 3

(√ x - 3 )2 = (3)2

x - 3 = 9

x = 12

Check:

√ x - 3 - 3

√ 12 - 3 - 3

3 - 3

0

0

Therefore, the solution

is x = 12.

x ≥ 3

L.S. R.S.

Slide 4

Radical Equations

Slide 5

Radical Equations

Slide 6

Radical Equations

Slide 7

Radical Equations

Slide 8

Solving Radical Equations

Solving Radical Equations

4 + √ 4 + x2 = x

√ 4 + x2 = x - 4

4 + x2 = x2 - 8x + 16

8x = 12

x

Since

the solution of

x =

is extraneous. Therefore,

there are no real roots.

Check:

(√ 4 + x2)2 = (x - 4)2

Slide 9

Solving Radical Equations

Slide 10

Solving Radical Equations

Slide 11

Solving Radical Equations

Slide 12

x = -1 is an extraneous solution.

x = -1 is an extraneous solution.

Slide 13

Set up the equation so that

Set up the equation so that

there will be one radical on

each side of the equal sign.

Square both sides.

Simplify.

2x + 4 = x + 7

x = 3

Verify your solution.

Therefore, the

solution is

x = 3.

x ≥ -2

Solve

Solving Radical Equations

L.S. R.S.

Slide 14

Squaring a Binomial

Squaring a Binomial

(a + 2)2 = a2 + 4a + 4

Note that the middle term is

twice the product of the two

terms of the binomial.

(a√x + b)2

( 5 + √x - 2 )2

The middle term will

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