Question

if (8/15)^3-(1/3)^3-(1/5)^3=x/75, find x..with explanation

Answer 1

Answer:

8

Step-by-step explanation:

Algebraic Identity Used:

$a^3 +b^3+c^3 =3abc \,\,\, if \,\,\, a+b+c =0$

Notice that

$\frac{8}{15}-\frac{1}{3} -\frac{1}{5} =0$

So, by identity, we have

$\left(\frac{8}{15}\right)^3-\left(\frac{1}{3} \right)^3 -\left(\frac{1}{5}\right)^3 = 3\times8/15\times1/3\times1/5=8/75$

Given that,

$\left(\frac{8}{15}\right)^3-\left(\frac{1}{3} \right)^3 -\left(\frac{1}{5}\right)^3 = 3\times8/15\times1/3\times1/5=8/75 = x/75\\\implies x=8$

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