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Popolare Algebra >

radici 1+x^8

Soluzione

radici

1 + x^{8}

Soluzione

x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i

Fasi della soluzione

1 + x^{8}

Le radici sono gli intercetti con l'asse x-assi

(y = 0)

1 + x^{8} = 0

Spostare

1

a destra dell'equazione

x^{8} = - 1

Riscrivi l'equazione con

u = x^{2}

e

u^{4} = x^{8}

u^{4} = - 1

Risolvi

u^{4} = - 1 : u = \frac{1}{2} + \frac{1}{2} i, u = - \frac{1}{2} - \frac{1}{2} i, u = - \frac{1}{2} + \frac{1}{2} i, u = \frac{1}{2} - \frac{1}{2} i

u = \frac{1}{2} + \frac{1}{2} i, u = - \frac{1}{2} - \frac{1}{2} i, u = - \frac{1}{2} + \frac{1}{2} i, u = \frac{1}{2} - \frac{1}{2} i

Sostituisci

u = x^{2},

risolvi per

x

Risolvi

x^{2} = \frac{1}{2} + \frac{1}{2} i : x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i

Risolvi

x^{2} = - \frac{1}{2} - \frac{1}{2} i : x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i

Risolvi

x^{2} = - \frac{1}{2} + \frac{1}{2} i : x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i

Risolvi

x^{2} = \frac{1}{2} - \frac{1}{2} i : x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i

Le soluzioni sono

x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i

Grafico

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