x²+1/x²+2-2x-2/x factorize
Answers
Answered by
1
Answer:
=(x+
x
1
)(x+
x
1
−2)
Step-by-step explanation:
\begin{gathered}Given ,\\x^{2}+\frac{1}{x^{2}}+2-2x-\frac{2}{x}\end{gathered}
Given,
x
2
+
x
2
1
+2−2x−
x
2
=x^{2}+\frac{1}{x^{2}}+2\times x \times \frac{1}{x}-2x-\frac{2}{x}=x
2
+
x
2
1
+2×x×
x
1
−2x−
x
2
=\big(x+\frac{1}{x}\big)^{2}-2\big(x+\frac{1}{x}\big)=(x+
x
1
)
2
−2(x+
x
1
)
=\big(x+\frac{1}{x}\big)\big(x+\frac{1}{x}-2\big)=(x+
x
1
)(x+
x
1
−2)
Therefore,
\begin{gathered}x^{2}+\frac{1}{x^{2}}+2-2x-\frac{2}{x}\\=\big(x+\frac{1}{x}\big)\big(x+\frac{1}{x}-2\big)\end{gathered}
x
2
+
x
2
1
+2−2x−
x
2
=(x+
x
1
)(x+
x
1
−2)
Answered by
1
Answer:
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