The area of a triangle is $$5$$. Two of its vertices are $$A\left( {2,1} \right)$$ and $$B\left( {3, - 2} \right)$$. The third vertex $$C$$ lies on $$y = x + 3$$. Find $$C$$.

One side of rectangle lies along the line $$4x + 7y + 5 = 0.$$ Two of its vertices are $$(-3, 1)$$ and $$(1, 1).$$ Find the equations of the other three sides.

Six X' s have to be placed in the squares of figure below in such a way that each row contains at least one X. In how many different ways can this be done.

Solve for $$x:{4^x} - {3^{^{x - {1 \over 2}}}}\, = {3^{^{x + {1 \over 2}}}}\, - {2^{2x - 1}}$$