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6.6 Solving Radical Equations

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Principle of power: If a = b then a n = b n for any n Question: Is it also true that if a n = b n then a = b? Explain in class.

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Steps on how to solve radical equations Get the radical term on one side (if there is only one radical term) Use the Principle of Power Check (this step is important, you have to do it when solving radical equations)

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1)x + 2 = 6 2) -3 + x = -9 3) 3 3x + 1 = 2 4) x – 7 + 3 = 10

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1)x + 2 = 6 x = 4 ( x) 2 = 4 2 x = 16 Check 2)-3 + x = -9 x = -6 Solution is an empty set because square root of a number can’t be negative 3) 3 3x + 1 = 2 3 3x = 1 ( 3 3x) 3 = 1 3 3x = 1 x = 1/3 check 4)x – 7 + 3 = 10 x – 7 = 7 ( x – 7) 2 = 7 2 x – 7 = 49 x = 56 check

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5) 3 x = x 6) 3 x = -3 7) 2x 1/2 - 7 = 9 8) 4 2x + 3 - 5 = -2

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5) 3 x = x (3 x) 2 = x 2 9x = x 2 0 = x 2 – 9x 0 = x(x – 9) So x = 0 or x = 9 check 6) 3 x = -3 ( 3 x) 3 = (-3) 3 x = -27 check 7) 2x 1/2 - 7 = 9 2 x = 16 x = 8 x 2 = 8 2 x = 64 8) 4 2x + 3 - 5 = -2 (4 2x + 3) 4 = 3 4 2x + 3 = 81 2x = 78 x = 39

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9) 2x-5 = 1 + x-310) x+5 - x-3 =2

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9)2x-5 = 1 + x-3 ( 2x-5) 2 = (1 + x-3) 2 2x-5 = 1 + 2 x-3 + x – 3 2x –x – 5 + 2 = 2 x-3 x – 3 = 2 x-3 (x – 3) 2 = (2 x-3) 2 x 2 – 6x + 9 = 4(x-3) x 2 – 6x + 9 = 4x-12 x 2 – 6x – 4x + 9 + 12 = 0 x 2 – 10x + 21 = 0 (x-7)(x-3) = 0 X = 7 or x = 3

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10) x+5 - x-3 =2 ( x+5 - x-3) 2 =2 2 x+5 -2 (x+5)(x-3) + x-3 = 4 2x + 2 -2 x 2 +2x-15 -4 = 0 2x – 2 = 2 x 2 +2x-15 (2x – 2) 2 = (2 x 2 +2x-15) 2 4x 2 -8x + 4 = 4(x 2 +2x-15) 4x 2 -8x + 4 = 4x 2 +8x-60 -16x = -64 x = 4

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There is another way for #10, isolate one radical term, then solve Try it!

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