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x +1/x=4 then find x^5+1/x^5=? Please hivee answer whith clearly

x +1/x=4 then find x^5+1/x^5=? Please hivee answer whith clearly

Grade:10

3 Answers

manna
59 Points
5 years ago
x+1/x=4
and we need to find x^5+1/x^5
first of all to make a power of 5 weneed to cube it.
(x+1/x)^3=4^3
apply formula (a+b)^3=a^3+b^3+3ab(a+b)
x^3+1/x^3+3x*1/x(x+1/x)=64
x^3+1/x^3+3*4   =64 Because x+1/x=4 and x*1/x=1
x^3+1/x^3+12=64
x^3+1/x^3=52
now we need to do  is
(x^3+1/x^3)^2=(52)^2
apply formula (a+b)^2=a^2+b^2+2ab
(x^3)^2+(1/x^3)^2+2x^3*1/x^3=2704
x^5+1/x^5+2=2704
x^5+1/x^5=2702---------hence answered
ROHIT mishra
13 Points
4 years ago
GivenX+1/x=3=a (let)X^2+1/x^2=a^2-2And X^3+1/x^3=a^3-3aThan x^5+1/x^5={x^2+1/x^2}×{x^3+1/x^3}-{x+1/x}I,e. 18×7-3=123
Shubham
11 Points
4 years ago
x+1/x=4x³+1/x³=52Multiplying both side by x²+1/x²(x³+1/x³)(x²+1/x²)=52(x²+1/x²)x^5+x+1/x^5+1/x=52*14x^5+1/x^5+4=728X^5+1/x^5=728-4=724

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