if x²+1/x=4,find the value of 2x³+2/x³
Answers
Given:
Answer:
Answer:
Given:
\textsf{$\dfrac{x^2+1}{x}\:=\:4$}
x
x
2
+1
=4
\textsf{a=1, b=-4 and c=1}a=1, b=-4 and c=1
Answer:
\textbf{Cross\: Multiplying}Cross Multiplying
\textsf{$x^2+1=4x$}x
2
+1=4x
\textsf{$x^2-4x+1=0$}x
2
−4x+1=0
\text < /strong > < strong > t < /strong > < strong > t < /strong > < strong > {Using Sridharacharya Method}</strong><strong>t</strong><strong>t</strong><strong>UsingSridharacharyaMethod
\texttt{$\dfrac{-b\:\pm\:\sqrt{b^2-4ac}}{2a}$}
2a
−b±
b
2
−4ac
\textbf{Substituting the value of a, b and c in the above formula}Substituting the value of a, b and c in the above formula
\textsf{x= $\dfrac{-(-4)\:\pm\:\sqrt{(-4)^2-4\times1\times1}}{2\times1}$}x=
2×1
−(−4)±
(−4)
2
−4×1×1
\textsf{x= $\dfrac{4\:\pm\:\sqrt{16-4}}{2}$}x=
2
4±
16−4
\textsf{x= $\dfrac{4\:\pm\:\sqrt{12}}{2}$}x=
2
4±
12
\textsf{x= $\dfrac{4\:+\:2\sqrt{3}}{2}\:\:\:or\:\:\:x=\:\dfrac{4\:-\:2\sqrt{3}}{2}$}x=
2
4+2
3
orx=
2
4−2
3
\textsf{x= $2(\dfrac{2+\sqrt{3}}{2})\:\:\:or\:\:\:x= 2(\dfrac{2-\sqrt{3}}{2})$}x= 2(
2
2+
3
)orx=2(
2
2−
3
)
\texttt{Substituting the value of $\sqrt{3}$ as 1.732}Substituting the value of
3
as 1.732
\textsf{x= 3.732 or x= 0.268}x= 3.732 or x= 0.268