Question

Find the value of \((\frac{21}{4-1})(\frac{23}{4}+\frac{21}{2}+\frac{21}{4}+1)\)

• A. 1
• B. 2
• C. 0
• D. 12

Answer 1

The Correct Option is A

Step 1: Define the variable

Let \( x = \frac{21}{4} \). This means that: 

We can rewrite the given expression as:

\[ x^4 = 2 \] \[ (x - 1)(x^3 + x^2 + x + 1) \]

Step 2: Recognizing the factorization

Observe that the expression \( (x - 1)(x^3 + x^2 + x + 1) \) is a standard factorization of the difference of cubes:

\[ (x - 1)(x^3 + x^2 + x + 1) = x^4 - 1 \]

Step 3: Substituting \( x^4 = 2 \) into the equation

Replacing \( x^4 \) with 2 in the equation:

\[ x^4 - 1 = 2 - 1 = 1 \]

Conclusion:

Thus, the value of the given expression is 1.