Question

Question 2(ii)
Represent the following situations in the form of quadratic equations.
(ii) The product of two consecutive positive integers is $306$. We need to find the integers.

Answer 1

(ii) Let the first integer number = $x$
Next consecutive positive integer will = $x+1$
Product of both integers = $x\times (x+1)=306$
⇒x2 +x=306\Rightarrow x^2 + x = 306⇒x2 +x=306
⇒x2 +x−306=0\Rightarrow x^2 + x - 306 = 0⇒x2 +x−306=0
⇒x2+18x−17x−306=0\Rightarrow x^2 +18 x -17 x - 306 = 0⇒x2+18x−17x−306=0
$\Rightarrow x(x+18)-17(x+18)=0$
$\Rightarrow (x+18)(x-17)=0$
Either $x+18=0orx-17=0$
$\Rightarrow x=-18orx=17$
Since, it's given integers are positive $x$ can only be $17$
$\therefore x+1=17+1=18$

Therefore, two consecutive positive integers will be $17$ and $18$.