Algebra MCQs

If x³ - 4x² + 19 = 6(x - 1) then what is the value of $$\left[ {{x^2} + \frac{1}{{x - 4}}} \right]?$$

If $${x^{x\sqrt x }} = {\left( {x\sqrt x } \right)^x}{\text{,}}$$    then x equals to?

If $$x + \sqrt 5 = 5 + \sqrt y $$     and x, y are positive integers, then the value of $$\frac{{\sqrt x + y}}{{x + \sqrt y }}$$   is?

If $$x - \frac{1}{x} = 1,$$   then what is the value of $$\frac{1}{x}\left( {\frac{1}{{x - 1}} - \frac{1}{{x + 1}} + \frac{1}{{{x^2} + 1}} - \frac{1}{{{x^2} - 1}}} \right)?$$

If $$x + \frac{1}{{16x}} = 3,$$   then the value of $$16{x^3} + \frac{1}{{256{x^3}}}$$   is:

If x + y + z = 6, then the value of (x - 1)³ + (y - 2)³ + (z - 3)³ is?

If $$x + \frac{1}{x} = 3{\text{,}}$$   then the value of $$\left( {{x^5} + \frac{1}{{{x^5}}}} \right)\,{\text{is?}}$$

If $${{\text{7}}^x}{\text{ = }}\frac{1}{{343}}{\text{,}}$$   then the value of x is?

If a + b + c = 3 and none of a, b and c is equal to 1, then what is the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)}} + \frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)}} + \frac{1}{{\left( {1 - c} \right)\left( {1 - a} \right)}}?$$