Question

X + x⁻¹ =√7
CALCULE : S = x⁴ + x⁻⁴

Answer 1

X + 1/x = sqrt (7)

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Hallamos X^4
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x+ 1/x = sqrt(7)

x^2+1  
--------- = sqrt(7)   
x
   
x^2+1 = sqrt(7)* x  

(x^2+1)^2 = 7*x^2

x^4 +2x^2 +1 = 7*x^2

x^4 = 5*x^2-1
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Hallamos X^-4
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1/x = = sqrt(7)-x
(1/x )^4 = (sqrt(7)-x)^4

x^-4 = x^4-4*sqrt(7)*x^3 + 42*x^2 -28*sqrt(7)*x + 49

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Encontramos eñ valor de S
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S = x^4 + x^-4
S = (5x^2-1) + (x^4-4*sqrt(7)*x^3 + 42*x^2 -28*sqrt(7)*x + 49)
S = x^4-4*sqrt(7)*x^3 + 47*x^2 -28*sqrt(7)*x  +48

Saludos :D