Question : If, for a non-zero $x, 5 x^2+7 x+5=0$, then the value of $x^3+\frac{1}{x^3}$ is:
Option 1: $\frac{496}{125}$
Option 2: $\frac{532}{343}$
Option 3: $\frac{125}{532}$
Option 4: $\frac{182}{125}$
Correct Answer: $\frac{182}{125}$
Solution :
Given, $5 x^2+7 x+5=0$
⇒ $5x^2+5 = -7x$
Dividing both sides by $5x$, we get,
⇒ $x+\frac{1}{x}=-\frac{7}{5}$ -----------------(1)
Cubing both sides, we get,
⇒ $x^3+\frac{1}{x^3}+3(x+\frac{1}{x})=-\frac{343}{125}$
⇒ $x^3+\frac{1}{x^3}+3(-\frac{7}{5})=-\frac{343}{125}$
⇒ $x^3+\frac{1}{x^3}=-\frac{343}{125}+\frac{21}{5}$
$\therefore x^3+\frac{1}{x^3}=\frac{182}{125}$
Hence, the correct answer is $\frac{182}{125}$.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
