Archie Deetoo
New member
- Joined
- Mar 11, 2018
- Messages
- 5
The question is :
Solve the given equation:
sqr root (3x+2) = 3x
I squared both side and then set to zero and ended up with:
(3x+1)(3x-2)=0
x = -1/3, 2/3
Now because I squared both sides in solving, I need to check for extraneous roots.
I checked x = 2/3 and got:
sqr root (3 (2/3) +2)) ?=? 3(2/3)
sqr root (4) = 2 : which is correct, so that is a correct root,
Now I checked x=-1/3:
sqr root (3(-1/3) +2)) ?=? 3(-1/3)
sqr root (1) = -1. That is also correct because square root of 1 is positive 1 and negative 1. So it appears both are correct and not extraneous solutions, yet the answer is 2/3 only. Why is that?
I have graphed the equation and can see that 2/3 is the correction solution and I can see by graphing that the extraneous solution is introduced when I square both sides when solving it. It seems that square root of 1 is only positive 1 on this occasion which is why -1/3 is extraneous.
I suppose what this comes down to is why is sometimes the square root of a number a positive answer and sometimes a positive and negative answer depending on the problem?
I appreciate any help with this.
Thanks a lot.
Zen
Solve the given equation:
sqr root (3x+2) = 3x
I squared both side and then set to zero and ended up with:
(3x+1)(3x-2)=0
x = -1/3, 2/3
Now because I squared both sides in solving, I need to check for extraneous roots.
I checked x = 2/3 and got:
sqr root (3 (2/3) +2)) ?=? 3(2/3)
sqr root (4) = 2 : which is correct, so that is a correct root,
Now I checked x=-1/3:
sqr root (3(-1/3) +2)) ?=? 3(-1/3)
sqr root (1) = -1. That is also correct because square root of 1 is positive 1 and negative 1. So it appears both are correct and not extraneous solutions, yet the answer is 2/3 only. Why is that?
I have graphed the equation and can see that 2/3 is the correction solution and I can see by graphing that the extraneous solution is introduced when I square both sides when solving it. It seems that square root of 1 is only positive 1 on this occasion which is why -1/3 is extraneous.
I suppose what this comes down to is why is sometimes the square root of a number a positive answer and sometimes a positive and negative answer depending on the problem?
I appreciate any help with this.
Thanks a lot.
Zen