Download presentation

Presentation is loading. Please wait.

1
**Solving Radical Equations and Inequalities**

Section 5.4 beginning on page 262

2
**Solving Radical Equations**

Step 1: Isolate the radical on one side. Step 2: Raise each side to the same power to eliminate the root. Step 3: Solve the resulting equation. Step 4: Check your answers for extraneous solutions. Example 1: Solve a) 2 𝑥+1 =4 2 𝑥+1 =2 ( 𝑥+1 ) 2 = 2 2 𝑥+1=4 2 𝑥+1 =4 𝑥=3 =4 2 4 =4 2(2)=4

3
**Solving Radical Equations**

Step 1: Isolate the radical on one side. Step 2: Raise each side to the same power to eliminate the root. Step 3: Solve the resulting equation. Step 4: Check your answers for extraneous solutions. Example 1: Solve b) 3 2𝑥−9 −1=2 3 2𝑥−9 =3 ( 3 2𝑥−9 ) 3 = 3 3 2𝑥−9=27 2𝑥=36 3 2(18)−9 −1=2 𝑥=18 3 36−9 −1=2 3 27 −1=2 3−1=2

4
**Extraneous Solutions Example 3: Solve 𝑥+1= 7𝑥+15 𝑥+1= 7𝑥+15 𝑥+1= 7𝑥+15**

𝑥+1= 7𝑥+15 𝑥+1= 7𝑥+15 𝑥+1= 7𝑥+15 7+1= 7(7)+15 −2+1= 7(−2)+15 (𝑥+1) 2 = ( 7𝑥+15 ) 2 8= −1= −14+15 𝑥 2 +2𝑥+1=7𝑥+15 8= 64 −1≠ 1 𝑥 2 −5𝑥−14=0 Since the radical is in the original problem, we are only looking for the principal (positive) root. 𝑥−7 𝑥+2 =0 𝑥=7 𝑥=7, 𝑥=−2

5
**Solving Equations With Two Radicals**

Example 4: Solve 𝑥+2 +1= 3−𝑥 𝑥+2 =−𝑥 ( 𝑥+2 ) 2 = (−𝑥) 2 ( 𝑥+2 +1) 2 = ( 3−𝑥 ) 2 𝑥+2+2 𝑥+2 +1=3−𝑥 𝑥+2= 𝑥 2 0= 𝑥 2 −𝑥−2 𝑥+2 𝑥+2 +3=3−𝑥 0=(𝑥−2)(𝑥+1) 2 𝑥+2 =−2𝑥 2 𝑥=2,𝑥=−1 𝑥=−1 Check: (2)+2 +1= 3−2 (−1)+2 +1= 3−(−1) 4 +1= 1 1 +1= 4 2+1≠1 1+1=2

6
**Solving an Equation with a Rational Exponent**

Example 5: Solve Step 1: Isolate what is being raised to a power. Step 2 : Raise each side to the reciprocal power. Step 3: Solve the resulting equation. Step 4: Check solution(s). 2𝑥 =10 2𝑥 =8 2𝑥 = 2𝑥= ( 3 8 ) 4 2𝑥= (2) 4 2𝑥=16 2(8) =10 𝑥=8 =10 𝑥=8 2 3 +2=10 8+2=10

7
**Solving a Radical Inequality**

** The same rules apply when we solve inequalities except: If you multiply or divide both sides by a negative, flip the inequality. An even root can not be less than 0. We must consider the possible values of the radicand We now know that 𝑥≤17 but there are values less than 17 that will not work here (due to the even root), so we need to find out what will work. Example 7: Solve 3 𝑥−1 ≤12 3 𝑥−1≥0 𝑥≥1 𝑥−1 ≤4 𝑥−1 2 ≤ 4 2 1≤𝑥≤17 𝑥−1≤16 𝑥≤17

8
**Monitoring Progress Solve the equation. Check your solution(s).**

1) 3 𝑥 −9=−6 2) 𝑥+25 =2 3) 2 3 𝑥−3 =4 5) 10𝑥+9 =𝑥+3 6) 2𝑥+5 = 𝑥+7 7) 𝑥+6 −2= 𝑥−2 8) 3𝑥 =−3 9) 𝑥 =𝑥 10) 𝑥 =8 11) Solve (a) 2 𝑥 −3≥3 and (b) 4 3 𝑥+1 <8 𝑥=27 𝑥=−21 𝑥=11 𝑥=27 𝑎𝑛𝑑 𝑥=0 𝑥=2 𝑥=3 𝑥=−9 𝑥=3 𝑥=14 𝑥≥9 𝑥<7

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google