if x²+1/x²=12, find the value of x=1/x
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Answer:
If x+1/x=12 , find the value of x^2+1/x^2
Answer:
x^2 + \frac{1}{x^2} = 142x
2
+
x
2
1
=142
Solution:
Given,
x + \frac{1}{x} = 12x+
x
1
=12
Use the following algebraic identity,
a^2 + b^2 = (a+b)^2 - 2aba
2
+b
2
=(a+b)
2
−2ab
Then,
\begin{gathered}x^2 + \frac{1}{x^2} = (x + \frac{1}{x})^2 - 2 \times x \times \frac{1}{x} \\\\x^2 + \frac{1}{x^2} = (x + \frac{1}{x})^2 - 2\\\\Substitute\ x + \frac{1}{x} = 12\\\\x^2 + \frac{1}{x^2} = 12^2 - 2\\\\x^2 + \frac{1}{x^2} = 144 - 2\\\\x^2 + \frac{1}{x^2} = 142\end{gathered}
x
2
+
x
2
1
=(x+
x
1
)
2
−2×x×
x
1
x
2
+
x
2
1
=(x+
x
1
)
2
−2
Substitute x+
x
1
=12
x
2
+
x
2
1
=12
2
−2
x
2
+
x
2
1
=144−2
x
2
+
x
2
1
=142
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