Question

the product of two consecutive positive integer is 306 . we need to find integers

Answer 1

Let the first number is x.

So, another number = ( x + 1 ).

A/Q,

 Product of integers = 306

  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

  So, x = -18 or 17.

But it is given that x is a positive integer , so x = 17.

1st number = x = 17.

Another number = x + 1 = 17 + 1 = 18.

Two consecutive integers whose sum is 306 are 17 and 18.

Answer 2

$\large\sf{Let,}$

$\small\sf{1st\:integer=x}$

$\small\sf{2nd\:integer=(x+1)}$

$\small\sf{product=306}$

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$\large\sf{A/C,}$

$\small\sf{x(x+1)=306}$

$\small\sf{{x}^{2}+x=306}$

$\small\sf{{x}^{2}+x-306=0}$