Question:
If (3x-\(\frac{1}{3x}\))=4, , then what is the value of (27x3-\(\frac{1}{27x^3}\)) ?
If (3x-\(\frac{1}{3x}\))=4, , then what is the value of (27x3-\(\frac{1}{27x^3}\)) ?
Updated On: Sep 13, 2024
- 52
- 64
- 48
- 76
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The Correct Option is D
Solution and Explanation
The correct option is (D): 76.
We know, (a – b)3 = a3 - b3 - 3ab(a –b)
Now, \((3x-\frac{1}{3x})^3=(27x^3-\frac{1}{27x^3})-3(3x)(\frac{1}{3x})(3x-\frac{1}{3x})\)
\(4^3=(27x^3-\frac{1}{27x^3})-3*4\)
\((27x^3-\frac{1}{27x^3})\)=76
We know, (a – b)3 = a3 - b3 - 3ab(a –b)
Now, \((3x-\frac{1}{3x})^3=(27x^3-\frac{1}{27x^3})-3(3x)(\frac{1}{3x})(3x-\frac{1}{3x})\)
\(4^3=(27x^3-\frac{1}{27x^3})-3*4\)
\((27x^3-\frac{1}{27x^3})\)=76
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