4find x from 1st quadratric
& use it in 2nd
If x+\frac{1}{x}=5 then the numerical value of x^{7}+\frac{1}{x^{7}} is,
A) 57965 B) Is a multiple of 7 C) 57695 D) Is a multiple of 5
[ multiple options correct]
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5 Answers
1have u tried your method.I have and it is lengthy is their any shortcut.
4i havent tried
ya mine is lengthy
but shorter may be by using binomial expansion
i'll post it after solving
11\left(x^3+\frac{1}{x^3} \right)=\left(x+\frac{1}{x} \right)^3-3\left(x+\frac{1}{x} \right) =125-15=110.
\left(x^5+\frac{1}{x^5} \right)=5^5- \binom {5}{1} \left(x^3+\frac{1}{x^3} \right)-\binom {5}{2}\left(x+\frac{1}{x} \right)
Now \left(x^7+\frac{1}{x^7} \right)=5^7-7(5^7-550-50)-(21.110) -350....which is the ans.