The value of ( x+1/x)² is:
Answers
Step-by-step explanation:
x² + ¹/ₓ² + 2
Given
\bullet \;\; \rm \bigg(x+\dfrac{1}{x}\bigg)^2∙(x+
x
1
)
2
To Find
Value of the givenx² + ¹/ₓ² + 2
Given
\bullet \;\; \rm \bigg(x+\dfrac{1}{x}\bigg)^2∙(x+
x
1
)
2
To Find
Value of the given
Formula
\bullet \;\; \rm (a+b)^2=a^2+b^2+2ab∙(a+b)
2
=a
2
+b
2
+2ab
Solution
\begin{gathered}\rm Compare\ given\ with\ (a+b)^2\ ,we\ get\ ,\\\\\implies \rm a=x\ ,b=\dfrac{1}{x}\end{gathered}
Compare given with (a+b)
2
,we get ,
⟹a=x ,b=
x
1
So ,
\begin{gathered}\rm \bigg(x+\dfrac{1}{x}\bigg)^2\\\\\implies \rm x^2+\bigg(\dfrac{1}{x}\bigg)^2+2.x.\dfrac{1}{x}\\\\\implies \rm x^2+\dfrac{1}{x^2}+2\end{gathered}
(x+
x
1
)
2
⟹x
2
+(
x
1
)
2
+2.x.
x
1
⟹x
2
+
x
2
1
+2
Formula
\bullet \;\; \rm (a+b)^2=a^2+b^2+2ab∙(a+b)
2
=a
2
+b
2
+2ab
Solution
\begin{gathered}\rm Compare\ given\ with\ (a+b)^2\ ,we\ get\ ,\\\\\implies \rm a=x\ ,b=\dfrac{1}{x}\end{gathered}
Compare given with (a+b)
2
,we get ,
⟹a=x ,b=
x
1
So ,
\begin{gathered}\rm \bigg(x+\dfrac{1}{x}\bigg)^2\\\\\implies \rm x^2+\bigg(\dfrac{1}{x}\bigg)^2+2.x.\dfrac{1}{x}\\\\\implies \rm x^2+\dfrac{1}{x^2}+2\end{gathered}
(x+
x
1
)
2
⟹x
2
+(
x
1
)
2
+2.x.
x
1
⟹x
2
+
x
2
1
+2