Beginning Algebra, 11th Edition

Using the Squaring Property Twice

Solve

Square each side.

Subtract 9. Subtract x.

Divide by 6.

Square each side again.

Apply the exponents.

CHECK Original equation

Let

5 = 5 ✓ True

225  3 + 2

221 + 4  3 + 24 x=4.

221 +x= 3 + 2 x

4 =x

22 = A 2 xB

2

2 = 2 x

12 = 62 x

21 +x= 9 + 62 x+x

A 221 +xB

2

= A 3 + 2 xB

2

221 +x= 3 + 2 x

221 +x= 3 + 2 x.

EXAMPLE 7

SECTION 8.6 Solving Equations with Radicals 535

CAUTION When squaring each side of

in Example 6,the entirebinomial must be squared to get

It is incorrect to square the 2xand the 1 separately to get 4x^2 +1.

2 x+ 1 4 x^2 + 4 x+1.

29 x= 2 x+ 1

The solution set is 546. NOW TRY

OBJECTIVE 4 Solve radical equations having cube root radicals.We d o

this by extending the concept of raising both sides of an equation to a power.

Solving Equations with Cube Root Radicals

Solve each equation.

(a)

Cube each side.

Apply the exponents.

Subtract 3x.

Divide by 2.

CHECK Original equation

Let

✓ True

The solution set is E^12 F.

B

3

5

2

=

B

3

5

2

x=^12.

B

35 a

1

2

b

B

33 a

1

2

b + 1

235 x= 233 x+ 1

x=

1

2

2 x= 1

5 x= 3 x+ 1

(^) A 235 xB
3
= A 233 x+ (^1) B
3
235 x= 233 x+ 1
EXAMPLE 8
NOW TRY
EXERCISE 7
Solve.
2 x+ 2 = 2 x+ 8
NOW TRY ANSWER

7. 516

Be careful here.