$[3, 7]$
$R$
$[2, 6]$
$[1, 4]$
Consider the following two statements
$I$. Any pair of consistent liner equations in two variables must have a unique solution.
$II$. There do not exist two consecutive integers, the sum of whose squares is $365$.Then,
Let $\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \mathrm{x}_4$ be the solution of the equation $4 x^4+8 x^3-17 x^2-12 x+9=0$ and $\left(4+x_1^2\right)\left(4+x_2^2\right)\left(4+x_3^2\right)\left(4+x_4^2\right)=\frac{125}{16} m$. Then the value of $\mathrm{m}$ is..........
Let $\alpha$ and $\beta$ be two real numbers such that $\alpha+\beta=1$ and $\alpha \beta=-1 .$ Let $p _{ n }=(\alpha)^{ n }+(\beta)^{ n },p _{ n -1}=11$ and $p _{ n +1}=29$ for some integer $n \geq 1 .$ Then, the value of $p _{ n }^{2}$ is .... .
The number of roots of the equation $|x{|^2} - 7|x| + 12 = 0$ is
The number of the real roots of the equation $(x+1)^{2}+|x-5|=\frac{27}{4}$ is ....... .