Algebra MCQs

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

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

If α and β are the roots of equation x² + αx + β = 0 then find α³ + β³ = ?

If a, b, c are non - zero $$a + \frac{1}{b} = 1$$   and $$b + \frac{1}{c} = 1,$$   then the value of abc is?

If p³ - q³ = (p - q){(p -q)² + xpq}, then the value of x is?

$$\frac{{\frac{1}{3}.\frac{1}{3}.\frac{1}{3} + \frac{1}{4}.\frac{1}{4}.\frac{1}{4} - 3.\frac{1}{3}.\frac{1}{4}.\frac{1}{5} + \frac{1}{5}.\frac{1}{5}.\frac{1}{5}}}{{\frac{1}{3}.\frac{1}{3} + \frac{1}{4}.\frac{1}{4} + \frac{1}{5}.\frac{1}{5} - \left( {\frac{1}{3}.\frac{1}{4} + \frac{1}{4}.\frac{1}{5} + \frac{1}{5}.\frac{1}{3}} \right)}}{\text{ is?}}$$

If $$x - \frac{1}{x} = 2{\text{,}}$$   then the value of the following is $${x^3} - \frac{1}{{{x^3}}}$$   = ?

If $${x^2} + {y^2} = 29$$   and xy = 10 where x > 0, y > 0, x > y, then the value of $$\frac{{x + y}}{{x - y}}$$   is?

If x³ + 27y³ + 64z³ = 36xyz, then the relationship between x, y and z is: