Algebra MCQs

If $${\text{ }}x - \sqrt 3 - \sqrt 2 = 0$$    and $$y - \sqrt 3 + \sqrt 2 {\text{,}}$$    then the value of $$\left( {{x^3} - 20\sqrt 2 } \right) - $$   $$\left( {{y^3} + 2\sqrt 2 } \right)?$$

If $$x + \frac{1}{x} = 1,$$   then the value of $$\frac{2}{{{x^2} - x + 2}} = \,?$$

If a² + b² + c² + 3 = 2(a + b + c) then the value of (a + b + c) is?

The value of the expression $$\frac{{{{\left( {a - b} \right)}^2}}}{{\left( {b - c} \right)\left( {c - a} \right)}} + $$   $$\frac{{{{\left( {b - c} \right)}^2}}}{{\left( {a - b} \right)\left( {c - a} \right)}} + $$    $$\frac{{{{\left( {c - a} \right)}^2}}}{{\left( {a - b} \right)\left( {b - c} \right)}}$$   = ?

If $$x + \frac{1}{{x + 1}} = 1,$$    then $${\left( {x + 1} \right)^5}$$   + $$\frac{1}{{{{\left( {x + 1} \right)}^5}}}$$   equals?

If $$a = \frac{{{b^2}}}{{b - a}}{\text{,}}$$   then the value of a³ + b³ is?

If x⁴ + y⁴ + x² + y² = $$17\frac{1}{{16}}$$ and x² - xy + y² = $$5\frac{1}{4},$$ then one of the values of (x - y) is:

If $${y^4} + \frac{1}{{{y^4}}} = 223$$   and y > 1, then find the value of $${y^2} + \frac{1}{{{y^2}}}?$$

If x = -2k and y = 1 - 3k, then for what value of k, will be x = y?