Q5 of 168 Page 7

The sum of two numbers is 18 and the sum of their reciprocals is . Find the numbers.

Let the first number be ‘X’, so the other number will be ’(18–X)’.

On simplifying further,

–X² + 18X – 72 = 0

X² – 18X + 72 = 0

On applying Sreedhracharya formula

X = 6 or X = 12

∴ The numbers are 6 & 12.

Find two consecutive positive integers, the sum of whose squares is 365.

The difference of two numbers is 4. If the difference of their reciprocals is , find the two numbers.

The sum of the squares of three consecutive positive integers is 50. Find the integers.

Find three consecutive positive integers such that the sum of the square of the first and the product of the other two is 154.