In the following question, two equations are given. You have to solve them and establish the relation between $x$ and $y$.

I. $x^2 + 14x + 49 = 0$
II. $2y^2– 17y + 36 = 0$

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is $20 \mathrm{years}$. Four years ago, the product of their ages in years was $48.$

A motor boat whose speed is $18 \mathrm{km}/\mathrm{hour}$ in still water takes $1 \mathrm{hour}$ more to go $24 \mathrm{km}$ upstream than to return downstream to the same spot. If the speed of the stream is $x \mathrm{km}/\mathrm{hour}$, find $x$.

Find two consecutive odd positive integers, sum of whose square is $290$.

The sum of the areas of two squares is $400 sq.m.$ If the difference between their perimeters is $16m$, find the sides of two squares

The sum of a number and its reciprocal is $\frac{26}{5}$. Find the number.