R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 7: EXERCISE 4.7

Find two consecutive odd positive integers, sum of whose squares is $970$. 

The difference between two natural numbers is $3$ and the difference of their reciprocals is $\frac{3}{28}$. Find the numbers.

The sum of the squares of two consecutive odd numbers is $394$. Find the numbers.

The sum of the squares of two consecutive multiples of $7$ is$637.$Find the multiples. 

The sum of the squares of two consecutive even numbers is $340$. Find the numbers.

The numerator of a fraction is $3$ less than the denominator. If $2$ is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is $\frac{29}{20}$. Find the original fraction.

Find a natural number whose square diminished by $84$ is equal to thrice of $8$ more than the given number.

A natural number which when increased by $12$ equals $160$ times its reciprocal. Find the number.