Math Book Cambodia: September 2022

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Sunday, September 11, 2022

If $x+1/x=2$ Find the value of $x^5+1/x^5$

If $x+1/x=2$ Find the value of $x^5+1/x^5$

As we had: $x+1/x=2$ $rightarrow(x+1/x)^2=4$ $leftrightarrowx^2+1/x^2=2$

We continue with $(x^2+1/x^2)(x+1/x)=4$ $leftrightarrowx^3+x+1/x+1/x^3=4$

$leftrightarrowx^3+1/x^3=2$

Friday, September 9, 2022

Vietnamese Olympiad 2022: Find the value of $1/(a^2023)+1/(b^2023)+1/(c^2023)$

If $a+b+c=2022$ and $1/a+1/b+1/c=1/2022$ Find the value of $1/(a^2023)+1/(b^2023)+1/(c^2023)$

Solution

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