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sqrt(cospix-1)=(x-1)(x-2) la ecuación

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Solución numérica:

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Solución

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\/ cos(pi*x) - 1  = (x - 1)*(x - 2)
$$\sqrt{\cos{\left(\pi x \right)} - 1} = \left(x - 2\right) \left(x - 1\right)$$
Gráfica
Respuesta numérica [src]
x1 = 2.0 - 3.09829651040851e-18*i
x2 = 2.0 + 2.29767785567574e-15*i
x3 = 2.0 - 7.66174303059679e-17*i
x4 = 2.0 + 7.15944809287606e-19*i
x5 = 2.0 + 2.63307702959348e-19*i
x6 = 2.0 + 4.58667143968498e-16*i
x7 = 2.0 + 2.15335512521794e-16*i
x8 = 2.0 - 5.36857456223657e-18*i
x9 = 2.0 - 7.29171126984027e-18*i
x10 = 2.0
x11 = 2.0 + 2.84010564700799e-19*i
x12 = 2.0 - 7.3656800562854e-19*i
x13 = 2.0 - 2.82247443546005e-16*i
x14 = 2.0 - 1.0139413738356e-16*i
x15 = 2.0 + 7.53318385204485e-18*i
x16 = 2.0 + 1.05968058132965e-18*i
x17 = 2.0 + 1.69045646373091e-18*i
x18 = 2.0 - 1.08601069989421e-18*i
x19 = 2.0 + 2.04204193368802e-18*i
x20 = 2.0 + 6.58507240332201e-19*i
x21 = 2.0 + 3.48119465918159e-17*i
x22 = 2.0 + 5.94839036680852e-19*i
x23 = 2.0 + 6.8571159480854e-17*i
x24 = 2.0 - 5.25360720463106e-19*i
x25 = 2.0 + 1.57004528598623e-18*i
x26 = 2.0 - 2.15691651971087e-18*i
x27 = 2.0 - 5.74027527528702e-18*i
x28 = 2.0 + 4.51625517087447e-18*i
x29 = 2.0 - 2.21568033654756e-16*i
x30 = 2.0 + 7.96304783860753e-19*i
x31 = 0.370883364087106 + 0.42373038449974*i
x32 = 2.0 - 3.58765340664825e-19*i
x33 = 2.0 + 4.00723335582065e-18*i
x34 = 2.0 - 2.32185522688907e-19*i
x35 = 2.0 - 4.3506104323298e-19*i
x36 = 2.0 - 7.22268058595415e-17*i
x37 = 2.0 - 2.31535342590338e-19*i
x38 = 2.0 + 1.47180260983069e-15*i
x39 = 0.370883364087106 - 0.42373038449974*i
x40 = 2.0 - 5.95910244313781e-18*i
x40 = 2.0 - 5.95910244313781e-18*i