Question

Si x+1/x=3 hallar M=x⁴+1/x⁴​

Answer 1

Respuesta:

X+(1/X) = 3

X(X)+X(1/X) = 3(X)

X²+1 = 3X

X²+1-3X = 3X-3X

X²-3X+1 = 0

X = (-(-3))+-√((3)²-4(1)(1)))/(2×1)

X = ( 3+- √(9-4))/2

X = ( 3+-√(5))/2

X1 = (3-√(5))/2

X1 = 0,382 ( Aproximadamente )

X2 = (3+√(5))/2

X2 = 2,618 ( Aproximadamente )

M = X⁴+(1/X⁴) con X1 = 0,382 :

M = (0,382)⁴+(1/((0,382)⁴)) ; 0,382⁴ = 0,021 ( Aproximadamente )

M = (0,021)+(1/(0,021)) ; (1/(0,021)) = 47,619 ( Aproximadamente )

M = 0,021 + 47,619

M = 47,64

M = X⁴+(1/X⁴) con X2 = 2,618 :

M = (2,618)⁴+(1/(2,618)⁴) ; (2,618)⁴ = 46,976 ( Aproximadamente )

M = 46,976+(1/(2,618)⁴)

M = 46,976+(1/46,976) ; 1/46976 = 0,021 ( Aproximadamente )

M = 46,976+0,021

M = 46,997

R// Por tanto el valor de M = X⁴+(1/X⁴) , es tanto 47,64 y 46,977

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