Solving Quadratic Equation with Solutions x1 and x2: How to Calculate x1-3+x2-3?

[Matejxx1]

1.given the equation a(3x²+2x+1)=4x-6x²-4 with the solutions x₁ and x₂
a) let a=0 without solving the equation calculate x₁^-3+x₂^-3
the correct answer is supposed to be -7/2

Homework Equations

x₁+x₂=-b/a
x₁*x₂=c/a

The Attempt at a Solution

The first thing I was that I put in "a" so,
0*(3x²+2x+1)=4x-6x²-4
0=4x-6x²-4...... here I multiplied the whole equation by -1
0=6x²-4x+4......here i divided the equation by 6
0=x²-4/6x+46
then I used the equation
1/x₁³+1/x₂³=(1/x₁+1/x₂)³ -3/x₁²x₂ -3/x₂²x₁
This is where I have no idea how to continue.I'm not even sure that what I have written is correct .If someone could help me solve this,I would really appreciate it. Thanks for reading .

 

[ehild]

1.given the equation a(3x²+2x+1)=4x-6x²-4 with the solutions x₁ and x₂
a) let a=0 without solving the equation calculate x₁^-3+x₂^-3
the correct answer is supposed to be -7/2

Homework Equations

x₁+x₂=-b/a
x₁*x₂=c/a

The Attempt at a Solution

The first thing I was that I put in "a" so,
0*(3x²+2x+1)=4x-6x²-4
0=4x-6x²-4...... here I multiplied the whole equation by -1
0=6x²-4x+4......here i divided the equation by 6
0=x²-4/6x+4/6
then I used the equation
1/x₁³+1/x₂³=(1/x₁+1/x₂)³ -3/x₁²x₂ -3/x₂²x₁
This is where I have no idea how to continue.I'm not even sure that what I have written is correct .If someone could help me solve this,I would really appreciate it. Thanks for reading .

Try to bring in x₁+x₂ and x₁x₂.
For example, $$1/x_1+1/x_2=\frac{x_1+x_2}{x_1 x_2}$$

ehild

 

[Matejxx1]

thank you for your reply. I did as you said and I got:
((x₁+x₂)/x₁x₂)³-3x₁/x₁²x₂² -3x₂/x₂²x₁². then I added the minuses together:
((x₁+x₂)/x₁x₂)³-3x₁+3x₂/(x₁x₂)²
Did I do this part correct?
May I also ask, what command did you use to write (x₁+x₂)/x₁x₂ because your way looks much easier to understand

 

[Ray Vickson]

thank you for your reply. I did as you said and I got:
(x₁+x₂/x₁x₂)³-3x₁/x₁²x₂² -3x₂/x₂²x₁². then I added the minuses together:
(x₁+x₂/x₁x₂)³-3x₁+3x₂/(x₁x₂)²
Did I do this part correct?
May I also ask, what command did you use to write x₁+x₂/x₁x₂ because your way looks much easier to understand

He did not write $x_1+x_2/x_1x_2$; you did that. In fact, you wrote
$$x_1 + \frac{x_2}{x_1 x_2}$$
If you mean
$$\frac{x_1 + x_2}{x_1 x_2}$$
then either use LaTeX or else use parentheses, like this: (x1+x2)/x1x2.

 

[Matejxx1]

He did not write $x_1+x_2/x_1x_2$; you did that. In fact, you wrote
$$x_1 + \frac{x_2}{x_1 x_2}$$
If you mean
$$\frac{x_1 + x_2}{x_1 x_2}$$
then either use LaTeX or else use parentheses, like this: (x1+x2)/x1x2.

Thank you I didn't notice that and I fixed it right away

 

[Matejxx1]

Now I added in the numbers
x₁+x₂=4/6
x₁*x₂=4/6
(((4/6)/4/6))-((3*4/6)/(4/6)² =
1-(2)/0,444=
1-4,5=-3,5=-7/2
Thank you very much for your help I got the right answer

 

[ehild]

You are welcome.

About using LaTeX, read https://www.physicsforums.com/showpost.php?p=3977517&postcount=3

ehild