Solve the given two equations and select the correct option.
$I.$ $9x^{2} - 114x + 361 = 0$
$II.$ $y^{2} = 36$

Let $a \ne b, c \ne 0$. If the equations $x^2 + ax + bc = 0$ and $x^2 + bx + ac = 0$ have a common root,then:
Statement $-1$: The equation of the other roots is $x^2 + cx + ab = 0$.
Statement $-2$: $a + b + c = 0$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $2.3x - 20.01 = 0$
$II.$ $2.9y - x = 0$

If $x^{2}+y^{2}+1=2x,$ then the value of $x^{3}+y^{5}$ is

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{3} \times 13 = x^{2} \times 247$
$II.$ $y^{1 / 3} \times 14 = 294 \div y^{2 / 3}$

Find two consecutive positive odd integers whose squares have the sum $290.$