Question

the difference between two positive numbers is 4 and difference of their cubes is 316.find the product​

Answer 1

Solution :

Let us assume two positive numbers a and b.

a - b= 4....(1)

a³-b³=316

This much is given in the question we just need to understand the question in order to write the steps given above.

Now,

We know that,

$(a - b) {}^{3} = a {}^{3} - b {}^{3} - 3ab(a - b)$

Now we have to substitute all the values in this identity.

$(4 {}^{3} ) = 316 - 3ab(4)$

$\implies64 = 316 - 12ab$

$\implies12ab - = 316 - 64$

$\implies12ab = 252$

$\implies \: ab = \frac{252}{12}$

$\implies \: ab = 21$

Therefore, The product will be 21