Question : If $x(x-5)=-1$, then the value of $x^3\left(x^3-110\right)=$?
Option 1: 0
Option 2: –1
Option 3: 1
Option 4: 2
Correct Answer: –1
Solution :
Given: $x(x-5)=-1$
⇒ $x-5=-\frac{1}{x}$
⇒ $x+\frac{1}{x}=5$
Cubing both sides, we get:
⇒ $(x+\frac{1}{x})^3=5^3$
⇒ $x^3+\frac{1}{x^3}+3(x\times\frac{1}{x})(x+\frac{1}{x})=125$
⇒ $x^3+\frac{1}{x^3}+3(x+\frac{1}{x})=125$
⇒ $x^3+\frac{1}{x^3}+3\times5=125$
⇒ $x^3+\frac{1}{x^3}=110$
⇒ $x^3-110=-\frac{1}{x^3}$
$\therefore x^3(x^3-110)=-1$
Hence, the correct answer is –1.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CPO
