Sign in
ui-button
ui-button
If \( \Large \left(x^{2}+\frac{1}{x^{2}}\right)=\frac{17}{4}\) , then what is \( \Large \left(x^{3}-\frac{1}{x^{3}}\right) \) equal to?
A) \( \Large \frac{75}{16} \)
B) \( \Large \frac{63}{8} \)
C) \( \Large \frac{95}{8} \)
D) None of the above.
Correct answer:
B) \( \Large \frac{63}{8} \)
Description for Correct answer:
\( \Large \left(x^{2}+\frac{1}{x^{2}}\right)=\frac{17}{4} \)
=>\( \Large x^{2}+\frac{1}{x^{2}}+2-2=\frac{17}{4} \)
=>\( \Large \left(x-\frac{1}{x}\right)^{2}+2=\frac{17}{4} \)
=>\( \Large \left(x-\frac{1}{x}\right)^{2}=\frac{17}{4}-2 \)
=>\( \Large \left(x-\frac{1}{x}\right)^{2}=\frac{3}{2} \)
On cubing both sides, we get
\( \Large \left(x-\frac{1}{x}\right)^{3}= \left(\frac{3}{2}\right)^{3} \)
=>\( \Large x^{3}-\frac{1}{x^{3}}-3 \times \frac{1}{x} \times \left(x-\frac{1}{x}\right)=\frac{27}{8} \)
=>\( \Large x^{3}-\frac{1}{x^{3}}=\frac{27}{8}+3 \times \frac{3}{2} \)
=>\( \Large x^{3}-\frac{1}{x^{3}}=\frac{27}{8}+\frac{9}{2} \)
=>\( \Large \left(x^{3}-\frac{1}{x^{3}}\right)=\frac{63}{8} \)
Please provide the error details in above question
Report Error
Recent Activities
General Knowledge
More questions and answers on- General Knowledge
Aptitude
More questions and answers on- Aptitude
Number System
More questions and answers on- Number System
Time and Distance
More questions and answers on- Time and Distance
Average
More questions and answers on- Average
Time and work
More questions and answers on- Time and work
Simple and compound interest
More questions and answers on- Simple and compound interest
Mensuration
More questions and answers on- Mensuration
Number series
More questions and answers on- Number series
Pipes and Cisterns
More questions and answers on- Pipes and Cisterns
Linear Equations
More questions and answers on- Linear Equations
Quadratic Equations
More questions and answers on- Quadratic Equations
Simplification
More questions and answers on- Simplification
Approximation
More questions and answers on- Approximation
Word problems
More questions and answers on- Word problems