SOLUTION: Can you please help me with this equation? 2m^(2/3)+3m^(1/3)-2=0, please show me the steps and get back asap (tonight if possible) Thanks so much

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you please help me with this equation? 2m^(2/3)+3m^(1/3)-2=0, please show me the steps and get back asap (tonight if possible) Thanks so much      Log On


   

Question 213355This question is from textbook
: Can you please help me with this equation?
2m^(2/3)+3m^(1/3)-2=0, please show me the steps and get back asap (tonight if possible)
Thanks so much This question is from textbook

Found 2 solutions by drj, MathTherapy:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Can you please help me with this equation?

2m%5E%282%2F3%29%2B3m%5E%281%2F3%29-2=0

Using the factoring approach we have the following

Step 1. Let +x=+m%5E%281%2F3%29
Then the 2m%5E%282%2F3%29%2B3m%5E%281%2F3%29-2=0 becomes an quadratic equation in x since m%5E%282%2F3%29=%28m%5E%281%2F3%29%29%5E2

2x%5E2%2B3x-2=0

Step 2. After trial and trial, we have

0=2x%5E2%2B3x-2=%282x-1%29%28x%2B2%29 we can verify using the FOIL method

Step 3. Now we have 2x-1=0 and x+2=0

2x-1=0

Add 1 to both sides to isolate x terms on left side

2x-1%2B1=0%2B1

2x=1

Divide 2 on both sides to get x

2x%2F2=1%2F2

x=1%2F2

Step 4. Now let's work

x%2B2=0

Subtract 2 from both sides to get x

x%2B2-2=0-2
x=-2

Step 5. Based on the above steps, x=0.5 and x=-2

Step 6. Since x=+m%5E%281%2F3%29 then

0.5=m%5E%281%2F3%29

0.5%5E3=%28m%5E%281%2F3%29%29%5E3

0.125=m

Now for x=-2

-2=m%5E%281%2F3%29

%28-2%29%5E3=%28m%5E%281%2F3%29%29%5E3

m=-8

Step 5. ANSWER: So m = 0.125 and -8.

The following steps show how to solve the above quadratic equation using the quadratic formula.

Step 1. Let +x=+m%5E%281%2F3%29

Then the 2m%5E%282%2F3%29%2B3m%5E%281%2F3%29-2=0 becomes an quadratic equation in x since m%5E%282%2F3%29=%28m%5E%281%2F3%29%29%5E2

2x%5E2%2B3x-2=0

Step 2. Then we use the quadratic formula to x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=2, b=3 and c=-2.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B3x%2B-2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A2%2A-2=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+25+%29%29%2F2%5C2+=+0.5
x%5B2%5D+=+%28-%283%29-sqrt%28+25+%29%29%2F2%5C2+=+-2

Quadratic expression 2x%5E2%2B3x%2B-2 can be factored:
2x%5E2%2B3x%2B-2+=+2%28x-0.5%29%2A%28x--2%29
Again, the answer is: 0.5, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-2+%29



Step 3 Based on the above steps, x=0.5 and x=-2

Step 4. Since x=+m%5E%281%2F3%29 then

0.5=m%5E%281%2F3%29

0.5%5E3=%28m%5E%281%2F3%29%29%5E3

0.125=m

Now for x=-2

-2=m%5E%281%2F3%29

%28-2%29%5E3=%28m%5E%281%2F3%29%29%5E3

m=-8

Step 5. ANSWER: So m = 0.125 and -8.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Can you please help me with this equation?
2m^(2/3)+3m^(1/3)-2=0, please show me the steps and get back asap (tonight if possible)
Thanks so much

2m%5E%282%2F3%29+%2B+3m%5E%281%2F3%29+-+2+=+0

%282m%5E%281%2F3%29+-+1%29%28m%5E%281%2F3%29+%2B+2%29+=+0 ------- Factor just like any ordinary trinomial
2m%5E%281%2F3%29+-+1+=+0, or, m%5E%281%2F3%29+%2B+2+=+0

2m%5E%281%2F3%29+=+1, or, m%5E%281%2F3%29+=+-+2

m%5E%281%2F3%29+=+1%2F2, or, m%5E%281%2F3%29+=+-+2
m%5E%281%2F3%29%5E3+=+%281%2F2%29%5E3, or, m%5E%281%2F3%29%5E3+=+%28-2%29%5E3 ----- Cubing both sides of the 2 equations

highlight_green%28m+=+1%2F8%29, or highlight_green%28m+=+-8%29