x2+1/x2=27 find the value of x+1/x
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Answer:
The value of \bold{x-\frac{1}{x} \text { is } 5}.
To find:
Find x-\frac{1}{x}
Solution:
Given: x^{2}+\frac{1}{x^{2}}=27
We know that (a-b)^{2}=a^{2}+b^{2}-2 a b
Putting a=x, b=\frac{1}{x}
\left(x-\frac{1}{x}\right)^{2}
=x^{2}+\frac{1}{x^{2}}-2 \times x \times \frac{1}{x}
=x^{2}+\frac{1}{x^{2}}-2
=27-2\ (Given\ that\ x^{2}+\frac{1}{x^{2}}=27)
=25
Hence, \left(x-\frac{1}{x}\right)^{2}=25
\left(x-\frac{1}{x}\right)^{2}=(5)^{2}
Taking square root of both sides, we get
\bold{x-\frac{1}{x}=5}
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