Transcript Solving Radical Inequalities

Solving Radical Inequalities
Solving Radical Inequalities
• Solving radical inequalities is similar to
solving rational equations, but there is
one extra step since we must make
sure the radical is a real number, i.e.
the radicand must be greater than or
equal to zero.
• Example 1
• Solve
x  2  3
• Since the radical
must be a real
number, x  2 must
be greater than or
equal to zero.
x20
x  2
• Square both
sides
 x+2   3
• Subtract 2 from
both sides
• We know that
both x  2 and
x  7 must be
true.
2
x29
x7
2
• Check a value of
in the original
inequality.
x
• The solution is all
real numbers such
that x  7 . [Note:
this takes care of
x  2 also]
x8
8  2  3
3.1623  3

• Example 2
• Solve
x  2  x  3
• Since each radical must be a real number,
for the first radical x  2  0 so x  2
and for the other radical x  0 .
x  0 makes both radicals real.
• Solve
x  2  x  3
• Isolate one radical
x  2  3  x
• Square both sides
 x  2   3  x 
• Simplify
x296 x  x
2
(continued on next slide)
2
(continued from previous slide)
• Isolate one variable
• Square both sides
• Simplify and solve
• Noting also that x  0 ,
the solution is 0  x  1.3611 ,
approximately .
7  6 x
7  6
2

2
x
49  36x
49
x
36
1.3611  x
• Check your answer
by substituting a
value for x in the
original inequality.
x 1
1  2  1  3
3  1  3
0.7321  3
