J P Mohindru and Bharat Mohindru Solutions for Chapter: Quadratic Equations, Exercise 7: EXERCISE

The difference of two numbers is $5$ and the difference of their reciprocals is $\frac{1}{10}$. Find the numbers.

Three consecutive positive integers are such that the sum of the square of the first and the product of other two is $46$, find the integers.

The difference of squares of two natural numbers is $45$. The square of the smaller number is $8$ times the larger number. Find the two numbers.

Note: The question given in the textbook seems to be wrong. The correct question should be as below:

The difference of squares of two natural numbers is $45$. The square of the smaller number is $4$ times the larger number. Find the two numbers.

A two-digit number is such that the product of the digits is $15$. If $18$ is added to the number, the digits are interchanged. Find the number.

Divide $16$ two parts such that twice the square of the larger part exceeds the square of the smaller part by $164$

A two-digit number is such that product of its digits is $14$. If $45$ is added to the number, the digits interchange the places. Find the number.

The denominator of a fraction is $3$ more than its numerator. The sum of the fraction and its reciprocal is $2\frac{9}{10}$. Find the fraction.

The sum of first $n$ even natural number is given by the relation $S=n (n+1)$. Find $n$ if the sum is $420$.