4.3 Solve Radical Equations NOTES - Algebra 2 Common...

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4.3SolveRadicalEquationsEx1: Ex2:ExtraneousSolutions:Ex3: Ex4:Ex5:

NOTES

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Ex6: Ex7:Ex8:YouTry!1) 2)

SUMMARY:

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4.3SolveRadicalEquations

Directions:Solvetheequation.Checkyouranswer.1)2 + 𝑟 = 11 2) 𝑥! − 10 = −3

3) 5𝑥 − 1! + 6 = 10 4)−5 𝑥 + 1 + 12 = 2

5) 2 8𝑥! + 9 = 5 6) 3𝑥! − 8𝑥 + 13 = 3

PRACTICE

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7) 22 − 3𝑥 = 𝑥 − 6 8)𝑥 = 2 + 7𝑥 − 6

9) 𝑏 − 7 = 9 − 𝑏 10)3 = 𝑥 + 𝑥 + 3

11)1 + 6𝑥 − 6 = 𝑥 12) 𝑚! + 2𝑚 + 1 = 5

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Directions:UsetheRemainderTheoremtofindtheremainderforeachofthefollowingdivisions.

UsetheFactorTheoremtodetermineif𝑥 + 1 isafactorofthefollowing:

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15) −2𝑥! − 4𝑥! + 𝑥 − 10

4.3SolveRadicalEquations

Directions:Solvetheequation.Checkyouranswer.1) 𝑥 − 2! + 5 = 8 2)𝑥 + 𝑥 = 6

3)ConsidertherighttriangleABCshowtotheright,withAB=8,andBC=x.a.Writeanexpressionforthelengthofthehypotenuseintermsofx.b.FindthevaluesofxforwhichAC–AB=9

WRAP UP

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4)CALCULATOR:Useyourgraphingcalculatorandfindtheintersectionofthefollowingtwoequations:𝑦! = 2𝑥𝑦! = 𝑥 + 3a)SketchthegraphbelowANDlabelthesolution.b)ALGEBRAICALLY:Whatextraneoussolutionariseswhentheequation2𝑥 = 𝑥 + 3issolvedforxbyfirstsquaringbothsidesoftheequation?c)JUSTIFY:Explainwhythereisanextraneoussolutionbyreferencingboththegraphicalandalgebraicsolutions.USECOMPLETESENTENCES!EXIT TICKET –

Explain why you need to always check for extraneous solutions when solving SQUARE root equations in complete sentences.

Will there ever be extraneous solutions when solving CUBE root equations? Explain why or why not?

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