The least integral value $\alpha $ of $x$ such that $\frac{{x - 5}}{{{x^2} + 5x - 14}} > 0$ , satisfies
${\alpha ^2} + 3\alpha - 4 = 0$
${\alpha ^2} - 5\alpha + 4 = 0$
${\alpha ^2} - 7\alpha + 6 = 0$
${\alpha ^2} + 5\alpha - 6 = 0$
If $x$ is real, then the maximum and minimum values of the expression $\frac{{{x^2} - 3x + 4}}{{{x^2} + 3x + 4}}$ will be
If $x$ be real, then the maximum value of $5 + 4x - 4{x^2}$ will be equal to
If $a$ and $b$ are the roots of equation $x^2-7 x-1=0$, then the value of $\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}$ is equal to $........$.
If $x, y$ are real numbers such that $3^{(x / y)+1}-3^{(x / y)-1}=24$ then the value of $(x+y) /(x-y)$ is
Let $a, b, c, d$ be real numbers such that $|a-b|=2$, $|b-c|=3,|c-d|=4$. Then, the sum of all possible values of $|a-d|$ is