If $x$ is real,then the maximum and minimum values of the expression $\frac{x^2 + 14x + 9}{x^2 + 2x + 3}$ are

If $x$ is real,the expression $\frac{x + 2}{2x^2 + 3x + 6}$ takes all values in the interval

If $ax + by = 1$,where $a, b, x$ and $y$ are integers,then which one of the following is not true?

If $\alpha, \beta$ are the roots of the equation $x^2 - px + q = 0$,then the quadratic equation whose roots are $(\alpha^2 - \beta^2)(\alpha^3 - \beta^3)$ and $\alpha^3\beta^2 + \alpha^2\beta^3$ is (where $S = p[p^4 - 5p^2q + 5q^2]$ and $P = p^2q^2(p^4 - 5p^2q + 4q^2)$).

The number of triples $(x, y, z)$ of real numbers satisfying the equation $x^4+y^4+z^4+1=4xyz$ is

The equation of lowest degree with rational coefficients having roots $\sqrt{3}+\sqrt{2} i$ and $\sqrt{3}-\sqrt{2}$ is