The product of two consecutive positive integers is 306. Find the integers.
Let the integers be x and x+1X*(x+1)=306X^2+x-306=0Apply any formula of quadratic equation then find x Which is 17,18
17,18
The product of two consecutive positive integers is 306. Find the integers
The product of two consecutive positive integers is 306. Find the integers
Let the two consecutive positive integers be x and (x + 1)
According to the given condition,
x(x + 1) = 306
⇒ x2 + x – 306 = 0
⇒ x2 + 18x – 17x – 306 = 0
⇒ x(x + 18) – 17(x + 18) = 0
⇒ (x + 18)(x – 17) = 0
⇒ x + 18 = 0 or x – 17 = 0
⇒ x = – 18 or x = 17
∴ x = 17 (x is a positive integers)
When x = 17,
x + 1 = 17 + 1 = 18
Hence, the required integers are 17 and 18.