Lesson 39 Sections 7.6 and 8.1Solving Radical EquationsUsing the Principle of Square Roots to Solve an Equation3xYou 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.92xIs 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 ba , then 22ba 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)623 xBefore squaring, the radical must be isolated.17)52 x18)751 a19)472 x120)1212x21)2134 xxA Quadratic Equation is any equation that can be written in the form 02 cbxax.You have already learned one way to solve a quadratic equation, using factoring as in the following example.312 1302 0130)2)(13(025352322xxxxxxxxxxxYou 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 Roots2Principle of Square Roots:For any real number k, if kxkxkx or then 2.Use the principle of square roots to solve these two quadratic equations.1)92x2)0232yThe principle of square roots can be generalized. X = a quantityIf kXkXkX or then 23)36)3(2x4)12)2(2n5) If 2)12()( xxf, find any values of x such that 11)(
View Full Document
Unlocking...