Question

m=a^1/3+a^-1/3 then the value of m^3-3m in red of a is​

Answer 1

m=1

See steps

Step by Step Solution:

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "m2"   was replaced by   "m^2".  1 more similar replacement(s).

Step by step solution :

STEP

1

:

Equation at the end of step 1

 (((m3) -  3m2) +  3m) -  1  = 0  

STEP

2

:

Checking for a perfect cube

2.1    m3-3m2+3m-1  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  m3-3m2+3m-1  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  3m-1  

Group 2:  -3m2+m3  

Pull out from each group separately :

Group 1:   (3m-1) • (1)

Group 2:   (m-3) • (m2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

2.3    Find roots (zeroes) of :       F(m) = m3-3m2+3m-1

Polynomial Roots Calculator is a set of methods aimed at finding values of  m  for which   F(m)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  m  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -1.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -8.00      

     1       1        1.00        0.00      m-1  

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

  m3-3m2+3m-1  

can be divided with  m-1

sorry if it was too long u can make it short