Question

There are two natural numbers such that the square of the smaller number exceeds five times the larger number by 4. Additionally, the sum of these two numbers is 20. Find the product of these two numbers.

Q: Answer-There are two natural numbers such that the square of the smaller number exceeds five times the larg...

Let the smaller number be a and larger number be b. a b 20 -------- I And, a2 5b 4 Or, a2 5 X 20 - a 4 from equation I Or, a2 100 - 5a 4 Or, a2 5a - 104 0 Or, a2 13a - 8a - 104 0 Or, aa 13 - 8a 13 0 Or, a - 8 a 13 0 So, a 8 or a - 13 But given that both are natural numbers, So, a 8 On putting value of a in equation I, We get, b 20 - 8 12 Therefore, required product 12 X 8 96