Equations with Radicals

Equations with Radicals

Equations with Radicals Solving equations with radicals requires following a few rules.

x–5 3 To eliminate a radical from an equation, both sides of the equation are squared.

Equations with Radicals Solving equations with radicals requires following a few rules.





2

x–5 3

2

To eliminate a radical from an equation, both sides of the equation are squared.

Equations with Radicals Solving equations with radicals requires following a few rules.

x–59 To eliminate a radical from an equation, both sides of the equation are squared.

Equations with Radicals Solving equations with radicals requires following a few rules.

x–59 When we eliminate radicals like this, we must be careful of extraneous roots.

Equations with Radicals Solving equations with radicals requires following a few rules.

x–59 Extraneous roots are solutions that appear correct but do not actually solve the equation.

Equations with Radicals Solving equations with radicals requires following a few rules.

x–59 This is why you should ALWAYS check a solution in the original equation.

Radical Equations Which one of these is a radical equation? Why?

x4 69

79  x 8

The equation on the left is a radical equation.

Radical Equations Which one of these is a radical equation? Why?

x4 69

79  x 8

Radical equations contain a variable in the radicand. The equation on the right is not a radical equation.

Solving Radical Equations Step 1: Isolate the radical on one side of the equation.

x5 2  4 x5  4– 2 x5  2

Solving Radical Equations Step 2: Eliminate the radical by squaring both sides of the equation.

x5 2  4 x5  4– 2



x5  2



x  5  2 2

x5  4

2

Solving Radical Equations Step 3: Solve for x.

x5 2  4 x5  4– 2



x5  2



x  5  2 2

2

x5  4 x  4–5 x  –1

Check solutions in the original equation

Solving Radical Equations Check solutions in the original equation

x  –1 x5 2  4 (–1)  5  2  4

424 22  4 44

Solve the following equation:

𝒙 + 𝟏𝟐 = 𝒙

Solve the following equation:

𝒙 + 𝟏𝟐 = 𝒙 Checking Solutions

Simplify following expression: Solve thethe following equation:

3+ 𝒙+𝟗=x a. b. c. d.

x=0 x=7 x = 0, x = –7 x = 0, x = 7

Solve the following equation:

3+ 𝒙+𝟗=x

Solve the following equation:

3+ 𝒙+𝟗=x Checking Solutions