Question

Two numbers differ by $8$ and their product is $153$. The numbers are

• A. $9,-17$
• B. $-17,9$
• C. $17,9$
• D. $11,19$

Answer 1

The correct option is C $17,9$

Let the larger number be $x$.

According to the given condition, smaller number would be $x-8$

Hence,
$x(x-8)=153$
$x^2-8x=153$
$x^2-8x-153=0$
$x^2-17x+9x-153=0$
$x(x-17)+9(x-17)=0$
$(x+9)(x-17)=0$
$x=-9$ and $x=17$
Since the numbers are positive.
Hence the larger number is 17.
While the smaller number is $17-8=9$.