Question

plz solve this problem

Answer 1

numbers are 2 and 7 . Their difference of their cubes are 343-8=335

Answer 2

Let the two numbers be $x \text {and} y$.

Then,

$|x-y| = 5$

and

$xy = 14$
We need the value of $|x^{3}-y^{3}|$

Note that Here I have used the absolute value function as we don't know which one of x and y is greater. If x>y then x-y would be greater than 0 and if y>x then x-y would be less than 0.
So x-y can either be 5 or -5.
So we are using absolute value function to only deal with the magnitude and not the sign.

Now,

$|x^{3}-y^{3}|$
$=|(x-y)(x^{2}+y^{2}+xy)|$
$=|(x-y)|×|(x^{2}+y^{2}+xy)|$
$=5×|(x^{2}+y^{2}+xy)|$
$=5×|(x^{2}+y^{2}-2xy+3xy)|$
$=5×|((x-y)^{2}+3xy)|$
$=5×|(25+3×14)|$
$= 335$