SOLUTION: Solve 12root3 + 2root3x = 4root6

Algebra ->  Expressions -> SOLUTION: Solve 12root3 + 2root3x = 4root6      Log On


   

Question 1041179: Solve 12root3 + 2root3x = 4root6
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
12%2Asqrt%283%29%2B2sqrt%283x%29=4%2Asqrt%286%29

2sqrt%283x%29=4sqrt%286%29-12sqrt%283%29

sqrt%283x%29=2sqrt%286%29-6sqrt%283%29

3x=4%2A6-24%2Asqrt%286%29sqrt%283%29%2B36%2A3

x=4%2A3-8%2Asqrt%2818%29%2B36

x=48-8sqrt%2818%29

x=48-8%2Asqrt%282%2A3%2A3%29

highlight%28x=48-72%2Asqrt%282%29%29, but this will be a negative number, so no solution.

What you originally wrote for your expression was not stated the way you really had as given to you. One of the other tutors already gave a solution.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Solve 12root3 + 2root3x = 4root6
If it's: 12sqrt%283%29+%2B+2sqrt%283x%29+=+4sqrt%286%29, then there's highlight_green%28matrix%281%2C3%2CNO%2C+REAL%2C+SOLUTIONS%29%29. 



Looking at the equation, 12sqrt%283%29, on the left, is larger than 4sqrt%286%29 on the right. Be reminded that 2sqrt%283x%29 is positive (> 0),

so how can you possibly take a larger number, add another number to it to get a smaller number? Makes absolutely NO SENSE.



Comment from student: I'm sorry, I submitted the question wrong. It's actually: Solve 12root3 + 2root3(x) = 4root6, so the x is not under the root sign. Sorry again!



12sqrt%283%29+%2B+2sqrt%283%29x+=+4sqrt%286%29

2sqrt%283%29%286+%2B+x%29+=+4sqrt%283%29+%2A+sqrt%282%29

2sqrt%283%29%286+%2B+x%29+=+2sqrt%283%29+%2A+2+%2A+sqrt%282%29

cross%282sqrt%283%29%29%286+%2B+x%29+=+cross%282sqrt%283%29%29+%2A+2+%2A+sqrt%282%29 ------ Factoring out GCF, 2sqrt%283%29

6+%2B+x+=+2sqrt%282%29

highlight_green%28matrix%281%2C3%2C+x+=+2sqrt%282%29+-+6%2C+or%2C+-3.171572875%29%29

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!



Plots y = 12%2Asqrt%283%29+%2B+2%2Asqrt%283x%29 and y = 4%2Asqrt%286%29

Comment from student: I'm sorry, I submitted the question wrong. It's actually: Solve 12root3 + 2root3(x) = 4root6,
so the x is not under the root sign. Sorry again!

My response: 
12%2Asqrt%283%29+%2B+2%2Asqrt%283%29%2Ax = 4%2Asqrt%286%29.

Divide both sides by 2%2Asqrt%283%29. You will get

6 + x = 2%2Asqrt%282%29.

Hence, x = 2%2Asqrt%282%29+-+6.

Answer.  x = 2%2Asqrt%282%29+-+6.

Solved.