If   $$x+{1\over x}=2 $$ then the value of    $$x^{12}-{1\over x^{12}} $$ is

If (3x – 2y) : (2x + 3y) = 5 : 6, then one of the values of $${\left({^3\sqrt { x}+\ ^3\sqrt { y}\over ^3\sqrt { x}-\ ^3\sqrt { y} } \right) \ }^2$$ is

If (m + 1) = √n + 3, the value of   $${1\over 2}\left({m^3-6m^2+12m-8\over \sqrt { n}}-n \right)  \ $$ is

If $${{p^2\over q^2}+{q^2\over p^2}}=1$$, then the value of (p⁶ + q⁶ ) is

If a + b – c = 0 then the value of 2b²c² + 2c²a² + 2a²b² –a⁴ – b⁴ – c⁴

$$4a-{4\over a}+3=0$$ then the value of :   $$ a^3-{1\over a^3}+3=?$$

If x² + y² + z² = 2 (x + z – 1), then the value of : x³ + y³ + z³ = ?

The HCF of x⁸ – 1 and x⁴ + 2x³ – 2x – 1 is :