Question

If the sum and the product of two numbers are 25 and 144 respectively, then the difference of the numbers must be

• A. $\pm 3$
• B. $\pm 5$
• C. $\pm 7$
• D. $\pm 11$

Answer 1

Answer: (C)

$\pm 7$

Let the two numbers are x and y, then by
hypothesis,
$x+y=25$
and $xy=144$
$\therefore (x-y{)}^2=(x+y{)}^2-4xy$
$=(25{)}^2-4\times 144$
$=625-576=49$
Hence $(x-y{)}^2=49$
$(x-y)=\pm 7$