Step 5 State the answer.Only the solution 8.5 makes sense in the original problem,
because if then
which cannot represent the time for the faster worker. The slower worker
could do the job in about 8.5 hr and the faster in about hr.
Step 6 Checkthat these results satisfy the original problem. NOW TRY
OBJECTIVE 3 Solve an equation with radicals by writing it in quadratic form.
Solving Radical Equations That Lead to Quadratic EquationsSolve each equation.
(a)
This equation is not quadratic. However, squaring each side of the equation gives
a quadratic equation that can be solved by factoring.
Square each side.Standard form
Factor.or Zero-factor property
or Proposed solutions
Squaring each side of an equation can introduce extraneous solutions. All proposed
solutions must be checked in the original (not the squared) equation.
CHECK
Let Let✓ True ✓ True
Both solutions check, so the solution set is
(b)
Isolate the radical on one side.
Square each side.
Standard form
Factor.or Zero-factor property
x= 4 or x= 9 Proposed solutions
x- 4 = 0 x- 9 = 0
1 x- 421 x- 92 = 0
x^2 - 13 x+ 36 = 0
x= 36 - 12 x+ x^2
2 x= 6 - x
x+ 2 x= 6
5 2, 4 6.
4 = 4 2 = 2
4 216 2 24
4 26142 - 8 x=4. 2 26122 - 8 x=2.
x= 26 x- 8 x = 26 x- 8
x= 4 x= 2
x- 4 = 0 x - 2 = 0
1 x- 421 x- 22 = 0
x^2 - 6 x+ 8 = 0
x^2 = 6 x- 8 A 2 aB^2 =a
x^2 = A 26 x- 8 B
2x= 26 x- 8
EXAMPLE 4
8.5- 1 =7.5
x- 1 = 0.5- 1 = -0.5,
x= 0.5,
SECTION 9.3 Equations Quadratic in Form 515
1 a-b 22 =a^2 - 2 ab+b^2CHECK
Let Let✓ True False
Only the solution 4 checks, so the solution set is 546. NOW TRY
6 = 6 12 = 6
4 + 24 6 x=4. 9 + 29 6 x=9.
x+ 2 x= 6 x + 2 x= 6
NOW TRY
EXERCISE 3
Two electricians are running
wire to finish a basement. One
electrician could finish the job
in 2 hr less time than the
other. Together, they complete
the job in 6 hr. How long
(to the nearest tenth) would it
take the slower electrician to
complete the job alone?
NOW TRY ANSWERS
3.13.1 hr
- (a) 5 4, 5 6 (b) 5166
NOW TRY
EXERCISE 4
Solve each equation.
(a)
(b)x+ 2 x= 20
x= 29 x- 20