Download Algebra II/Trig Honors Unit 3 Day 6: Solve Radical Equations

Algebra II/Trig Honors
Unit 3 Day 6: Solve Radical Equations
Objective: To solve radical equations
Definition:
 Radical Equation - ___________________________________________________________
Solving Radical Equations:
Step 1: Isolate the radical on one side of the equation
Step 2: Raise each side of the equation to the same power to eliminate the radical
Square both sides to eliminate square roots; cube both sides to eliminate cube roots
Step 3: Solve. Check your answer in the original equation.
Example 1: Solve a radical equation
Solve.
a.
3
2x  7  3
b.
x  25  4
Example 2: Solve a radical equation given a function
In a hurricane, the mean sustained wind velocity v (in meters per second) is given by
v p   6.3 1013  p where p is the air pressure (in millibars) at the center of the hurricane. Estimate
the air pressure at the center of a hurricane when the mean sustained wind velocity is 54.5 meters per
second.
Solving with Rational Exponents - _______________________________________________________
___________________________________________________________________________________
Example 3: Solve an equation with a rational exponent
Solve.
a. 4 x 2 3  36
b.  x  2 
34
1  7
Extraneous Solutions - ________________________________________________________________
___________________________________________________________________________________
To avoid extraneous solutions, you should always __________________________________________
Example 5: Solve an equation with an extraneous solution
Solve
a. x  1  7 x  15
b. 10 x  9  x  3
If an equation has two radicals, you may need to ___________________________________________
Example 6: Solve an equation with two radicals
Solve
a.
x  2 1  3  x
HW: Page 208 #3-51 (M3), 53
b.
x6 2 x2