In half-wave rectifier, what is the output frequency if

If x + y + z = 4, xyz = 6 & x² + y² + z² = 8 then find the value of x³ + y³ + z³.

If the ratio of the areas of two triangles is 4:3 and the ratio of their heights is 3:4, then the ratio of the lengths of their bases will be

(123×123×123 + 130×130×130)/(123×123 - 123×130 + 130×130) = ? 

Find the value of

(1 -  `1/(p+1)` ) + (1 - `2/(p+1)`  ) + (1 - `3/(p+1)`  ) + ........................... + (1 -  `p/(p+1)` )

If x² + x = 11

find (x+4)³ +1/((x+4)³)

If x² + px + q = 0 has roots 4 and -3, find the values of p and q.

If (x² + 1)/x = 3, what is the value of (x¹² + 1)/x ⁶ ?

If x = 19, then the value of x⁵ - 20x⁴ + 20x³ - 20x² + 20x - 1 is