Question

The product of two consecutive numbers is 72 . Use a quadratic equation to find the two sets of numbers.//

Answer 1

two sets of numbers are (-8 and -9) and (8 and 9)

Explanation:

The product of two consecutive numbers is 72

let x is the first number

x + 1 is the second number

x(x+1) = 72

x² + x - 72 = 0

(x+9)(x-8) = 0

x = -9, x = 8

Answer 2

Hello!

Answer:

`\Large \boxed{\sf (8~ and~ 9) ~and~(-8 ~and~ -9)}`

Explanation:

→ We want to find the sets of two numbers.

→ The numbers are:

`\sf x\\x + 1`

→ The product of the two numbers is:

`\sf x(x+1)`

→ So we have this equation:

`\sf x(x+1) = 72`

→ Let's solve this equation to find the sets of two numbers:

◼ Simplify the left side:

`\sf x^2 + x = 72`

◼ Put the equation to 0:

`\sf x^2 + x -72= 0`

→ It's a quadratic equation because it's on the form ax² + bx + c = 0.

→ To solve a quadratic equation, there is the quadratic formula:

`\sf x = (-b \pm√(b^2 - 4ac))/(2a)`

In our equation:

`\sf a = 1\\b = 1\\c = -72`

◼ Let's apply the quadratic formula:

`\sf x = (-1 \pm√(1^2 - 4(1)(-72)))/(2(1))`

◼ Simplify the equation:

`\sf x = (-1 \pm√(289))/(2)`

`\sf x = (-1 \pm17)/(2)`

→ So the two solutions are:

`\sf x_1 = (-1 +17)/(2) = (16)/(2) = 8`

`\sf x_2 = (-1 -17)/(2) = (-18)/(2) = -9`

The fisrt set is 8 and 9 because the consecutive number of 8 is 9.

The second set is -8 and -9 because the consecutive number of -9 is -8.

Conclusion:

The two sets of consecutive natural numbers whose product is 72 are 8 and 9, and -9 and -8.