Page 730 - Algebra 1

Some equations contain more than one radical expression. If possible, it is helpful to put the radical expressions on opposite sides of the equal sign.
Solving With Square Roots on Both Sides
Example
3
Solve each equation.
a. √ x+ 2=√ 2x + 4 SOLUTION
Use inverse operations.
Hint
When a single radical
is on each side, begin
by writing the equation without radical symbols.
√ x + 2 ( √ x + 2 ) 2 x+2 -__2 x -_ 2_x -x x
= √ 2 x + 4
= ( √ 2 x + 4 ) 2 =2x+4
= -__2
= 2x + 2
= -_ 2_x
= 2
= -2
Square both sides.
Simplify.
Subtraction Property of Equality Simplify.
Subtraction Property of Equality Simplify.
Multiply by -1.
C h e c k
√ x + 2 = √ 2 x + 4 √ -2 + 2 √ 2(- 2) + 4
√ 0 √ - 4 + 4 √ 0 √ 0
0=0✓
b . √ x + 2 - √ 2 x = 0 SOLUTION
Use inverse operations. √ x + 2 - √ 2 x = 0
+ √ 2 x = + √ 2 x ___ ___
√x + 2 =
( √ x + 2 ) 2 =
x+2 =
2 =
C h e c k √ x + 2 - √ 2 x = 0 √ 2 + 2 - √ 2 ( 2 ) 0 √ 4 - √ 4 0
0=0 ✓
-x =
__ __
√ 2x
( √ 2 x ) 2 2x
-x
x
Addition Property of Equality Simplify.
Square both sides.
Simplify.
Subtraction Property of Equality Simplify.
Lesson 106 715