Presentation on theme: "Aim: How do we solve radical equations?"— Presentation transcript:
1 Aim: How do we solve radical equations? Do Now: Describe the steps for solving:x2 – 80 = 0x2 = 80add 80 to both sidestake square root of both sidessimplifyDescribe the reverse processsquare both sidesx2 = 80x2 – 80 = 0subtract 80 from both sidesHow do we solve?solve by first squaringboth sides.
3 Simplifying RadicalsKEY: Find 2 factors for the radicand - one of which is the largest perfect square possibleMultiplying Radicals
4 Dividing RadicalsIf quotient is not a perfect squareyou must simplify the radicand.
5 Adding/Subtracting Radicals Must have same radicand and indexAdd or subtract coefficients and combine result with the common radicalCoefficientCommon RadicalCombined ResultUnlike radicals must first be simplifiedto obtain like radicals(same radicand-same index), if possible.ex.
6 Solving Radical Equations Solve and check:Isolate the radical:(already done)Square each side:Solve the derivedequation:x2 – 9x + 16 = 0use quadraticformula:
7 Solving Radical Equations Solve and check:Isolate the radical:(already done)Square each side:Solve the derivedequation:x – 2 = 25x = 27Check:(x – 2)1/2 = 5[(x – 2)1/2]2 = 52alternate:5 = 5
8 ? Extraneous Roots Solve and check: Isolate the radical: Square each side:Solve the derivedequation:2y – 1 = 92y = 10y = 5Check:y = 5 is an extraneous root;there is no solution!?3 + 7 = 4
9 Solving Radical Equations Solve and check:Isolate the radical:Square each side:Solve the derivedequation:x2 – 2x + 1 = x + 5x2 – 3x – 4 = 0(x – 4)(x + 1) = 0x = x = -1Checkeachroot:?4 = 4x = -1 is an extraneous root
10 Solving Radical Equations Solve and check:?Square each side:Solve the derivedequation:32(x – 2) = 22(x + 8)9(x – 2) = 4(x + 8)9x – 18 = 4x + 32x = 10x = 10 checks out as the solution
11 Model ProblemThe radical function is anapproximation of the height in meters ofa female giraffe using her weight x inkilograms. Find the heights of female giraffeswith weights of 500 kg. and 545 kg.Evaluate for 500:Evaluate for 545: 3.17 m. 3.27m.
12 Model ProblemThe equation gives the time T in seconds it takes a body with mass 0.5 kg to complete one orbit of radius r meters. The force F in newtons pulls the body toward the center of the orbit.a. It takes 2 s for an object to make one revolution with a force of 10 N (newtons). Find the radius of the orbit.b. Find the radius of the orbit if the force is 160 N and T = 2.a.