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Lesson39

# Lesson39 - 17 5 2 =-x 18 7 5 1-=-a 2 19 4 7 2-=-x 20 1 2 1...

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1 Lesson 39 Sections 7.6 and 8.1 Solving Radical Equations Using the Principle of Square Roots to Solve an Equation 3 = x You know you can add, subtract, multiply, or divide (by nonnegative number) and get a true equation. Let's see if both sides can be raised to the same power . Square both sides of the equation above. 9 2 = x Is x = 3 still a solution? Yes. However, 3 - could also be a solution of the squared equation. So raising both sides to the same power results in an equation with a solution of the original equation. However, sometimes there may also be solutions that are not solutions of the original equation. Power Rule: If b a = , then 2 2 b a = has the same solution as the original equation. However, the squared equation may also have 'extra' solutions that are not solutions of the original equation. Therefore, all solutions of a squared equation must be checked in the original equation. Solve the following equations. Check all solutions. 16) 6 2 3 = - x Before squaring, the radical must be isolated.

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Unformatted text preview: 17) 5 2 =-x 18) 7 5 1-=--a 2 19) 4 7 2-=--x 20) 1 2 1 2-=--x 21) 2 13 4 + = + x x A Quadratic Equation is any equation that can be written in the form 2 = + + c bx ax . You have already learned one way to solve a quadratic equation, using factoring as in the following example. 2 2 1 3 3 2 5 3 5 2 (3 1)( 2) 3 1 0 or 2 3 1 2 x x x x x x x x x x x- =-- = +-= + =- = = -= = -3 You will now learn another way to solve a quadratic equation. In lesson 40, you will learn a third way to solve quadratic equations. Using the Principle of Square Roots Principle of Square Roots: For any real number k , if k x k x k x-= = = or then 2 . Use the principle of square roots to solve these two quadratic equations. 1) 9 2 = x 2) 2 3 2 =-y The principle of square roots can be generalized. Q = a quantity If 2 then Q or Q Q k k k = = = -3) 36 ) 3 ( 2 = + x 4) 12 ) 2 ( 2 = + n 5) If 2 ) 1 2 ( ) (-= x x f , find any values of x such that 11 ) ( = x f ....
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