Question

The product of two positive consecutive integers is 462. Find the integers.

Answer 1

Step-by-step explanation:

for explanation refer to the attachment

Answer 2

Answer:

21 & 22

Step-by-step explanation:

Given: Product of two positive consecutive integers is 462.

To find integers.

Let integers be $x,(x+1)$.

According to question:

$x(x+1)=462\\x^{2} +x=462\\x^{2} +x-462=0$

Now splitting the middle term we have:

$x^{2} +22x-21x-462=0\\x(x+22)-21(x+22)=0\\(x-21)(x+22)=0$

This implies, $x=21,-22$ but $x=-22$ not possible as it is not positive.

Hence consecutive positive integers are 21 & 22.

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