SOLUTION: PLEASE HELP ME TO SOLVE THESE QUESTIONS............. Q1.IF {{{x^3+1/x^3=2}}} then find the value of x+1/x Q2.FIND THE VALUE OF {{{(x+y)^3+(x-2y+2)}}} Q3.IF {{{(x+1/x)*(x-1

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Question 353546: PLEASE HELP ME TO SOLVE THESE QUESTIONS.............
Q1.IF then find the value of x+1/x
Q2.FIND THE VALUE OF
Q3.IF .then find the value of



Found 2 solutions by Edwin McCravy, jsmallt9:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
PLEASE HELP ME TO SOLVE THESE QUESTIONS.............
Q1.IF then find the value of x+1/x
Using the binomial theorem:











and since we are given ,





Let , which is what we want to find.



Feasible rational roots are ±1, ±2
Using synthetic division we find that -1 is a solution

-1|1  0 -3 -2
  |  -1  1  2
   1 -1 -2  0

Thus we have factored



as



Factoring further:



Thus the solutions are y = -1, y = 2

so  is either -1 or 2.

-----------------------------------


Q2.FIND THE VALUE OF

Something is missing from this one that must be given 
to find a solution.  Check the problem again and repost 
it with the part that's missing here.

-----------------------------------

Q3.IF .then find the value of


Multiplying the first two factors:



Multiplying the first two factors:



Multiplying the first two factors:



Multiplying those factors:



Let 



Clear of fractions:





Factoring,



Solutions are , 

and since 

 or 

(In the case of the second negative solution, 
x would have to be imaginary).

Edwin


Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
Q1.IF then find the value of x+1/x
Let's start by eliminating the fraction. Multiply both sides by :

To solve a non-linear equation, we often get one side equal to zero and factor:

Solving this equation is much easier if we notice that the exponent of 6 is twice the exponent of 3. That makes this equation in quadratic form for . Looking at the expression this way we can, perhaps, see that the expression fits the pattern: which we know is, in factored form: . So you equation factors into:

By the Zero Product Property we know that this (or any) product is zero only if one of the factors is zero. So:

Solving this we get x = 1.
This makes x + 1/x = 1 + 1/1 = 1 + 1 = 2.

Q2.FIND THE VALUE OF
This problem does not make sense. You can't find a value unless you have an equation and this has no equals sign. The only thing you can do with this expression is simplify it. That means cubing (x+y) correctly (Hint: It is not !) and then combining like terms, if any.

Q3.IF .then find the value of
The first two factors fit the pattern of (a+b)(a-b) which we know from the pattern to be equal to . So your first two factors are equal to . But this and the third factor fit the same pattern again. So the first three factors are equal to . But this, combined with the next factor fit the pattern again. And this repeats once more time making the entire left side of the equation equal to:
. So now our equation looks like:

We can solve this just like we did problem 1. Get rid of the fraction:

Get one side equal to zero:

This, like problem 1, is an equation in "quadratic form". This time it is in quadratic form for . This equation, unlike problem 1, does not factor easily. When we can't factor, we resort to the Quadratic Formula. This gives us:

Simplifying.





In long form this is:
or
Looking at the second equation, we see that the fraction will be negative. And since cannot be equal to a negative number, there will be no solutions to the second equation. So we only have to solve the first equation. we continue by simplifying:



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