Q2 of 168 Page 7

Two numbers differ by 3 and their product is 504. Find the numbers.

Let the first number be ‘X’, so the other number will be ’(X+3)’.

∵ X(X + 3) = 504

X² + 3X– 504=0

On applying Sreedhracharya formula

X = –24 or 21.

∴ if the first number is – 24 , then the other number is – 21.

∴ if the first number is 21 , then the other number is 24.

∴ The numbers are not (21,24) & (– 21, – 24).

Prove that the equation x²(a² + b²) + 2x(ac + bd) + (c² + d²)= 0 has no real root, if ad ≠ bc.

Divide 12 into two parts such that their product is 32.

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.