Question

The difference of two positive numbers is $7$. Their product is $170$, what are the numbers?

• A. $8,15$
• B. $12,19$
• C. $15,22$
• D. $17,10$

Answer 1

The correct option is D $17,10$

Let the larger number be $x$.
Then the smaller number will be $(x-7)$
$x(x-7)=170$
$x^2-7x-170=0$
$x^2-77x+10x-170=0$
$x(x-17)+10(x+17)=0$
$(x-17)(x+17)=0$
Either, $x-17\Rightarrow x=17$
$x+10=0\Rightarrow x=-10$
But $x=-10$ is not positive number so it is not possible.
$\therefore x=17$
Larger number $=x=17$.
Smaller number is $x-7=17-10$
$\therefore$ The required number are $17$ and $10$.