Answers
Answer:
Answer: The required value of the given expression is 2.
Step-by-step explanation: We are given the following equality :
x+1x=2 (i)x+\dfrac{1}{x}=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)x+
x
1
=2 (i)
We are to find the value of the following expression :
x2+1x2.x^2+\dfrac{1}{x^2}.x
2
+
x
2
1
.
We will be using the following formula :
(a+b)2=a2+b2+2ab.(a+b)^2=a^2+b^2+2ab.(a+b)
2
=a
2
+b
2
+2ab.
Squaring equation (i) on both sides, we have
(x+1x)2=22⇒x2+(1x)2+2×x×1x=4⇒x2+1x2+2=4⇒x2+1x2=4−2⇒x2+1x2=2.\begin{lgathered}\left(x+\dfrac{1}{x}\right)^2=2^2\\\\\\\Rightarrow x^2+\left(\dfrac{1}{x}\right)^2+2\times x\times\dfrac{1}{x}=4\\\\\\\Rightarrow x^2+\dfrac{1}{x^2}+2=4\\\\\\\Rightarrow x^2+\dfrac{1}{x^2}=4-2\\\\\\\Rightarrow x^2+\dfrac{1}{x^2}=2.\end{lgathered}
(x+
x
1
)
2
=2
2
⇒x
2
+(
x
1
)
2
+2×x×
x
1
=4
⇒x
2
+
x
2
1
+2=4
⇒x
2
+
x
2
1
=4−2
⇒x
2
+
x
2
1
=2.
Thus, the required value of the given expression is 2.
Step-by-step explanation:
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Answer:
Step-by-step explanation:
