Question

The product of two consecutive numbers is 12. What are the numbers?

Answer 1

Answer:

required numbers are 3 and 4

Step-by-step explanation:

let n , (n+1) be the req. nos.

a/q, n(n+1) =12

=> n^2+n-12=0

=> n^2+4n-3n-12=0

=> n(n+4)-3(n+4)=0

=> (n-3)(n+4)=0

so, n =-4 or, 3

But ,n=-4 is not a natural nos.

Thus, n=3 & (n+1)=(3+1)=4

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Answer 2

Answer:

the two consecutive numbers are 3,4 (or) -3,-4

Step-by-step explanation:

• let the two consecutive numbers be x, (x - 1)
• product = 12

$x \times (x - 1) = 12 \\ {x}^{2} - x = 12 \\ {x}^{2} - x - 12 = 0 \\ {x}^{2} - 4x + 3x - 12 = 0 \\ x(x - 4) + 3(x - 4) = 0 \\ (x - 4)(x + 3) = 0 \\ x = 4 \: \: \: \: \: \: \: (or )\: \: \: \: \: \: x = - 3$

$if \: \: x = 4 \\ x - 1 = 4 - 1 = 3 \\ \\ if \: \: x = - 3 \\ x - 1 = - 3 - 1 = - 4$