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

x^5 + \\frac{1}{x^5} = (x^2 + \\frac{1}{x^2})(x^3 + \\frac{1}{x^3}) - (x + \\frac{1}{x} ) src=http://latex.codecogs.com/gif.latex?%3D%3E%20x%5E5%20+%20%5Cfrac%7B1%7D%7Bx%5E5%7D%20%3D%20%28x%5E2%20+%20%5Cfrac%7B1%7D%7Bx%5E2%7D%29%28x%5E3%20+%20%5Cfrac%7B1%7D%7Bx%5E3%7D%29%20-%20%28x%20+%20%5Cfrac%7B1%7D%7Bx%7D%20%29> x^5 + \\frac{1}{x^5} = (2)(3) - 1 src=http://latex.codecogs.com/gif.latex?%3D%3E%20x%5E5%20+%20%5Cfrac%7B1%7D%7Bx%5E5%7D%20%3D%20%282%29%283%29%20-%201> x^5 + \\frac{1}{x^5} = 5 src=http://latex.codecogs.com/gif.latex?%3D%3E%20x%5E5%20+%20%5Cfrac%7B1%7D%7Bx%5E5%7D%20%3D%205>

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Grade 11Algebra

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

ankit raj

10 Years agoGrade 11

8 Answers

Anoopam Mishra

10 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

10 Years ago

pa1

10 Years ago

RAJU

10 Years ago

SEELA YUVARAJU

10 Years ago

Raghu Vamshi Hemadri

10 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

10 Years ago

RAGHU

10 Years ago

$=> x^5 + \frac{1}{x^5} = (x^2 + \frac{1}{x^2})(x^3 + \frac{1}{x^3}) - (x + \frac{1}{x} )$ $=> x^5 + \frac{1}{x^5} = (x^2 + \frac{1}{x^2})(x^3 + \frac{1}{x^3}) - (x + \frac{1}{x} )$

$=> x^5 + \frac{1}{x^5} = (2)(3) - 1$

$=> x^5 + \frac{1}{x^5} = 5$