Question
The difference between two positive numbers is $4$ and the difference between their cubes is $316.$Find $:$ Their product
✓
Answer
Given difference between two positive numbers is $4$ and difference between their cubes is $316$.
Let the positive numbers be $a$ and $b$
$a - b = 4$
$a^3- b^3= 316$
Cubing both sides,
$(a - b)^3= 64$
$a^3- b^3- 3ab(a - b) = 64$ Given $a^3- b^3= 316$
So $316 - 64 = 3ab(4)$
$252 = 12ab$
So $ab= 21;$ product of numbers is $21$
Let the positive numbers be $a$ and $b$
$a - b = 4$
$a^3- b^3= 316$
Cubing both sides,
$(a - b)^3= 64$
$a^3- b^3- 3ab(a - b) = 64$ Given $a^3- b^3= 316$
So $316 - 64 = 3ab(4)$
$252 = 12ab$
So $ab= 21;$ product of numbers is $21$
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