Question

$x+\frac{2}{x}=3$ হলে, $x^3+\frac{8}{x^3}$ এর মান কত?

Answer 1

দেওয়া আছে, $x+\frac{2}{x}=3$

প্রদত্ত রাশি, $x^3+\frac{8}{x^3}$

$=\left(x\right)^3+\left(\frac{2}{x}\right)^3$

$=\left(x+\frac{2}{x}\right)^3-3\cdot x\cdot\frac{2}{x}\left(x+\frac{2}{x}\right)$

$=\left(x+\frac{2}{x}\right)^3-6\left(x+\frac{2}{x}\right)$

$=3^3-6\cdot3$

$=27-18$

$=9$ [Answer]

Comments

Rules Applied:

• $a^3+b^3=(a+b)^3-3ab(a+b)$