If the roots of the equation x² $$-$$ nx + m = 0 differ by 1, then

If a, b and c are the sides of a $$\Delta$$ABC, then $${a^{{1 \over p}}} + {b^{{1 \over p}}} - {c^{{1 \over p}}}$$, where p > 1, is

Read the following information carefully and answer the questions given below.

Let $$\alpha$$ and $$\beta$$ be the roots of the equation $${x^2} - (1 - 2{a^2})x + (1 - 2{a^2}) = 0$$.

Under what condition does the above equation have real roots?

Read the following information carefully and answer the questions given below.

Let $$\alpha$$ and $$\beta$$ be the roots of the equation $${x^2} - (1 - 2{a^2})x + (1 - 2{a^2}) = 0$$.

Under what condition is $${1 \over {{\alpha ^2}}} + {1 \over {{\beta ^2}}} < 1$$?