Note lecture mathematics sec v

Solving Radical Equations
operation of Tx is ✗
^
The So to solve radical
-
opposite .
, equations,
take the
power of the index n of both sides of the equation
to get rid
of the radicals .
We must check our solutions to make

that
sure
they work in the
original equation
Fito
Eg : Solve the
equation :
-

✗ = I

* In order
,
to
get rid of the square
-

root, we'll square both
sides ,
but first let's isolate the radical on one side of the

equation ( otherwise ,
we won't get rid of it when we square)
¥-10 = ✗ 1- I
(52×+0)
'
= 1×1-112
2×1-10 = ✗4-2×+1
0 = 2+2×+1
✗ -
2×-10
0=+2-9
0=1×-311×+31 { ✗ -3=0
✗ 1-3=0
✗=3
✗ =-3
Then ,
check solutions : -
It -
3 =
1 ? -
¥+10K 3) =/ ?
To -3 = 1 ? At 3=1 ?
4- 3 = 1 ✓ 21-3=16 false
so the see is ✗ =3
NO It be the case that we need to square both
may
-
:


sides multiple times in order to get rid of all the square
roots


la.GL?a2-2abtb2Lr2xiT--rxK=
.




Eg : Solve 52×+1 -
Fx = I
a
(1)
(5×+7) tlfxd =L
'
-

2A t lfx
2×+1 -
2 Tax + Fx 1- ✗ =L
Now isolate the root term & root
,
, sq again .




252×+7 Fx =-3 ✗ 1-25×+1
-
. rxK= C- 3×12
412×1-1 ) ✗ = 9×2=38×2+4 ✗ =qx2 ✗2-411=0 =) XCX -41=0
.




✗= 0,11=4