Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Document related concepts

no text concepts found

Transcript

Section 6-7 Solving Radical Equations Objective: 1. Solve equations containing radicals. Extraneous Solution When solving radical equations, the result may be a number that does not satisfy the original equation. Such a number is called an extraneous solution. I’m going to show you two ways to solve this equation. Method 1 Get the radical by itself – in this problem subtract 4 from both sides of the equation The opposite of taking the square root of a term is to square the term, so square both sides of the equation. Solve for x Check the answer! (This may be an extraneous solution) I’m going to show you two ways to solve this equation. Method 1 Get the radical by itself – in this problem subtract 4 from both sides of the equation The opposite of taking the square root of a term is to square the term, so square both sides of the equation. Solve for x Check the answer! (This may be an extraneous solution) – Substitute 7 for x in the original equation. Since you get the same answer on both sides of the equation, 7 is the correct answer. Method 2 Use a graphing calculator to solve the equation Type the left side of the equation in Y1 Type the right side of the equation in Y2 Graph the equations Calculate the intersection of the graphs – press: • 2nd • TRACE • Choose option 5: intersect x=7 Since the graphs intersect at the point (7, 7), the xvalue is the answer! – There is no need to check the solution since the graphs had an intersection point! Method 1 Square both sides to get rid of the radical on the left side – the radical on the right side will not be eliminated On the right side of the equals sign, multiply the term by itself – use the distributive property Combine like terms Subtract x from both sides Subtract 4 from both sides Divide both sides by -4 Square both sides Check the answer! Since the two sides are NOT equal, there is NO SOLUTION Method 2 Use a graphing calculator to solve the equation Type the left side of the equation in Y1 Type the right side of the equation in Y2 Graph the equations – You will have to change the window because the first graph moves to the right 12 units The graphs DO NOT INTERSECT, so there is NO SOLUTION! Method 1 Get the terms inside the parenthesis by themselves – add four to both sides and then divide both sides by 2 The opposite of raising something to the 1/3 power is to cube it – so cube both sides Solve for x Check the solution! Since you the same answer on both sides of the equation, the answer is correct Method 2 Use a graphing calculator to solve the equation Type the left side of the equation in Y1 Type the right side of the equation in Y2 (You don’t have to graph y = 0 because that is the same as the x-axis) Graph the equations Calculate the intersection of the graphs or find the zero if you didn’t graph the second equation On the home screen change the decimal to a fraction • X • MATH • 1: Fraction Use either method to solve Use either method to solve Method 1: Method 2: • Add 6 to both sides • Graph the equation(s) • Divide by 3 • Find the intersection • Raise both sides to the or the zero 4th power Choice C: n = 5 is the • Check the answer correct answer