Let a, b be the solutions of x² + px + 1 = 0 and c, d be the solution of x² + qx + 1 = 0. If (a $$-$$ c) (b $$-$$ c) and (a + d)(b + d) are the solution of x² + ax + $$\beta$$ = 0, then $$\beta$$ is equal to

If a$$\in$$R, b$$\in$$R, then the equation x² $$-$$ abx $$-$$ a² = 0 has

The solution of the inequality $${4^{ - x + 0.5}} - {7.2^{ - x}} < 4$$, x $$\in$$R is

Let x₁ and x₂ be the real roots of the equation $${x^2} - (k - 2)x + ({k^2} + 3k + 5) = 0$$, then maximum value of $$x_1^2 + x_2^2$$ is