Question

Solve: 9(x^2+1/x^2)-3(x-1/x) -20 = 0​

Answer 1

Explanation:

Three solutions were found :

 x = 2

 x = 1/2 = 0.500

 x = 1

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

Step by step solution :

Step  1  :

1 Simplify — x

Equation at the end of step  1  :

1 1 ((2•((x2)+————))-(9•(x+—)))+14 = 0 (x2) x

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  x  as the denominator :

x x • x x = — = ————— 1 x

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • x + 1 x2 + 1 ————————— = —————— x x

Equation at the end of step  2  :

1 (x2+1) ((2•((x2)+————))-(9•——————))+14 = 0 (x2) x

Step  3  :

Polynomial Roots Calculator :

 3.1    Find roots (zeroes) of :       F(x) = x2+1

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

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  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      2.00        1     1      1.00      2.00   

Polynomial Roots Calculator found no rational roots

Equation at the end of step  3  :

1 9•(x2+1) ((2•((x2)+————))-————————)+14 = 0 (x2) x

Step  4  :

1 Simplify —— x2