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x+1/x =1 , x 2 +1/x 2 =2 and x 3 +1/x 3 =3 then x 5 + 1/x 5 = what

x+1/x =1 ,
x2+1/x2 =2
and x3+1/x3=3
then  x5 + 1/x5 = what

Grade:11

8 Answers

Anoopam Mishra
126 Points
8 years ago
(x^2 + \frac{1}{x^2})(x^3 + \frac{1}{x^3}) = x^5 + \frac{1}{x^5} + x + \frac{1}{x}
=> x^5 + \frac{1}{x^5} = (x^2 + \frac{1}{x^2})(x^3 + \frac{1}{x^3}) - (x + \frac{1}{x} )
=> x^5 + \frac{1}{x^5} = (2)(3) - 1
=> x^5 + \frac{1}{x^5} = 5
HARINATH
90 Points
8 years ago
5
pa1
357 Points
8 years ago
5
RAJU
398 Points
8 years ago
5
SEELA YUVARAJU
226 Points
8 years ago
5
Raghu Vamshi Hemadri
72 Points
8 years ago
=> x^5 + \frac{1}{x^5} = (x^2 + \frac{1}{x^2})(x^3 + \frac{1}{x^3}) - (x + \frac{1}{x} )=> x^5 + \frac{1}{x^5} = (x^2 + \frac{1}{x^2})(x^3 + \frac{1}{x^3}) - (x + \frac{1}{x} )
=> x^5 + \frac{1}{x^5} = (2)(3) - 1
=> x^5 + \frac{1}{x^5} = 5
SHANMUKESHWAR
461 Points
8 years ago
5
RAGHU
38 Points
8 years ago
 
=> x^5 + \frac{1}{x^5} = (x^2 + \frac{1}{x^2})(x^3 + \frac{1}{x^3}) - (x + \frac{1}{x} )=> x^5 + \frac{1}{x^5} = (x^2 + \frac{1}{x^2})(x^3 + \frac{1}{x^3}) - (x + \frac{1}{x} )
=> x^5 + \frac{1}{x^5} = (2)(3) - 1
=> x^5 + \frac{1}{x^5} = 5

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