Question

The product of two consecutive natural number is 72. find the numbers​

Answer 1

Let the two consecutive natural numbers be x and (x+1).

From the given condition, we have

➾x(x+1 ) = 72

⇒x² +x = 72

⇒x² +x−72 = 0

⇒x² +9x − 8x − 72 = 0

⇒x(x+9) − 8(x+9) = 0

⇒(x−8)(x+9) = 0

⇒x − 8 = 0 or x + 9 = 0

⇒x = 8 or x = −9

∵−9 is not a natural number.

So, x = 8 and x + 1 = 8 + 1 = 9.

Hence, the numbers are 8 and 9

Answer 2

Answer:

The consecutive numbers are 8 and 9

Step-by-step explanation:

Let the numbers be x and x+1

So, x* (x+1) = 72

x² + x = 72

x² + x - 72 =0

x = {-b ± √(b² - 4ac) } / 2a

x = {-1 ± √(1² + 4×1×(-78)) } / 2×1

x = {-1 ± √(1 + 288) } / 2 = {-1 ± √289 } / 2

x = (-1 ± 17) / 2

If x= (-1 - 17) / 2

then x = -18/2 = -9 (not possible, ∵ -9 is not a natural number)

and if x = (-1 + 17) / 2

then x = 16/2 = 8

∴ x = 8

and if x= 8

then x+1 = 8+1 = 9

Hence, the consecutive numbers will be 8 and 9.

Hope this helps...