X-1/x=1 হলে x3-1/x3 এর মান কত

X-1/x=1 হলে \(x^{3}\)-1/\(x^{3}\) এর মান কত ?

Created: 8 months ago | Updated: 2 months ago | Created By:

farjana akter akter

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Institution: Directorate of Primary Education - DPE Exam: Primary Exam Question Solution 31-05-2019
Topic: Algebra (বীজগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem \( x - \frac{1}{x} = 1 \) and find the value of \( x^3 - \frac{1}{x^3} \), we can start by manipulating the given equation.

Firstly, let's denote \( y = x - \frac{1}{x} \), which gives us \( y = 1 \). We need to find \( x^3 - \frac{1}{x^3} \), and we can do this by using the identity:

\[
x^3 - \frac{1}{x^3} = (x - \frac{1}{x})^3 + 3(x - \frac{1}{x}
\)

Expanding this, we get:

\[
x^3 - \frac{1}{x^3} = y^3 + 3y
\]

Substituting \( y = 1 \):

\[
x^3 - \frac{1}{x^3} = 1^3 + 3(1) = 1 + 3 = 4
\]

Thus, the value of \( x^3 - \frac{1}{x^3} \) is \( 4 \). This leads us to conclude that the correct answer is option A) 4.0. This approach highlights the utility of algebraic identities in simplifying seemingly complex problems, allowing for quick evaluation of expressions.

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