Download 6-7 Solving Radical Equations and Inequalities - modified for online

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