Solve the following system of linear equations in three variables.
x + y + z = 6; 2x + 3y + 4z = 20;
3x + 2y + 5z = 22

Using quadratic formula solve the following equations.
p²x² + (P² -q²) X - q² = 0

Using quadratic formula solve the following equations.9x²-9(a+b)x+(2a²+5ab+2b²)=0

Find the values of k for which the following equation has equal roots.
(k - 12)r + 2(k - 12)x + 2 = 0

Prove that the equation x²(a²+b²)+2x(ac+bd)+(c²+ d²) = 0 has no real root if ad≠bc.