# Flicking through the pages

Algebra Level pending

There was a statement on a page on the book.

"$x_1$ and $x_2$ are the roots of the equation $\square_1 x^2 - mx + \square_2 = 0$, where $\square_1 \in \{m, n\}$ and $\square_2 \in \{m, n\}$ (with $mn > 0$ and $x_1 > x_2$). It is true that $\sqrt{\dfrac{x_1}{x_2}} + \triangle_1\sqrt{\dfrac{x_2}{x_1}} + \triangle_2\sqrt{\dfrac{m}{n}} = 0$, where $\triangle_1 \in \{-1, 1\}$ and $\triangle_2 \in \{-1, 1\}$."

Which of the following options is correct?

Option 1: $\square_1 = m, \square_2 = n, \triangle_1 = 1, \triangle_2 = -1$

Option 2: $\square_1 = m, \square_2 = n, \triangle_1 = -1, \triangle_2 = 1$

Option 3: $\square_1 = n, \square_2 = n, \triangle_1 = 1, \triangle_2 = -1$

Option 4: $\square_1 = n, \square_2 = n, \triangle_1 = 1, \triangle_2 = 1$

Option 5: $\square_1 = n, \square_2 = m, \triangle_1 = -1, \triangle_2 = 1$

Option 6: $\square_1 = n, \square_2 = m, \triangle_1 = 1, \triangle_2 = -1$

Option 7: $\square_1 = n, \square_2 = n, \triangle_1 = -1, \triangle_2 = 1$

Option 8: $\square_1 = n, \square_2 = n, \triangle_1 = -1, \triangle_2 = -1$

×