Harvard University Admission Interview Trick | How To Solve!!! |You Should Know This Trick!

[@stpat7614]

Including complex roots: a^6 - 4 = 0 a^(3*2) - 4 = 0 (a^3)^2 - 4 = 0 (a^3)^2 - 2^2 = 0 (a^3 - 2)(a^3 + 2) = 0 (a^3 - [2^(1/3)]^3)(a^3 + [2^(1/3)]^3) = 0 (a - 2^[1/3])(a^2 + a*2^[1/3] + [2^(1/3)]^2)(a + 2^[1/3])(a^2 - a*2^[1/3] + [2^(1/3)]^2) = 0 (a - 2^[1/3])(a^2 + a*2^[1/3] + 2^[1/3*2])(a + 2^[1/3])(a^2 - a*2^[1/3] + 2^[1/3*2]) = 0 (a - 2^[1/3])(a^2 + 2^[1/3]*a + 2^[2/3])(a + 2^[1/3])(a^2 - 2^[1/3]*a + 2^[2/3]) = 0 (a - 2^[1/3])(a + 2^[1/3])(a^2 + 2^[1/3]*a + 2^[2/3])(a^2 - 2^[1/3]*a + 2^[2/3]) = 0 a - 2^(1/3) = 0, or a + 2^(1/3) = 0, or 1*a^2 + 2^(1/3)*a + 2^(2/3) = 0, or 1*a^2 - 2^(1/3)*a + 2^(2/3) = 0 a - 2^(1/3) + 2^(1/3) = 0 + 2^(1/3), or a + 2^(1/3) - 2^(1/3) = 0 - 2^(1/3), a = (-2^[1/3] +/- sqrt[(2^[1/3])^2 - 4*1*2^(2/3)]) / (2*1), or a = (-(-2^[1/3]) +/- sqrt[(-2^[1/3])^2 - 4*1*2^(2/3)]) / (2*1) a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- sqrt[(2^[1/3])^2 - 4*2^(2/3)]) / (2), or a = (2^[1/3] +/- sqrt[(-2^[1/3])^2 - 4*2^(2/3)]) / (2) a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- sqrt[(2^2)^(1/3) - 4*(2^2)^(1/3)]) / 2, or a = (2^[1/3] +/- sqrt[(-1)^2*(2^2)^(1/3) - 4*(2^2)^(1/3)]) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- sqrt[4^(1/3) - 4*4^(1/3)]) / 2, or a = (2^[1/3] +/- sqrt[1*4^(1/3) - 4*4^(1/3)]) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- sqrt[4^(1/3) - 4*4^(1/3)]) / 2, or a = (2^[1/3] +/- sqrt[4^(1/3) - 4*4^(1/3)]) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- sqrt[4^(1/3)*(1 - 4)]) / 2, or a = (2^[1/3] +/- sqrt[4^(1/3)*(1 - 4)]) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- sqrt[4^(1/3)*(-3)]) / 2, or a = (2^[1/3] +/- sqrt[4^(1/3)*(-3)]) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- sqrt[(2^2)^(1/3)*3*(-1)]) / 2, or a = (2^[1/3] +/- sqrt[(2^2)^(1/3)*3*(-1)]) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- sqrt[2^(2*1/3)*3*(-1)]) / 2, or a = (2^[1/3] +/- sqrt[2^(2*1/3)*3*(-1)]) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- sqrt[2^(2/3)*3*(-1)]) / 2, or a = (2^[1/3] +/- sqrt[2^(2/3)*3*(-1)]) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- [2^(2/3)*3*(-1)]^[1/2]) / 2, or a = (2^[1/3] +/- [2^(2/3)*3*(-1)]^[1/2]) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- [2^(2/3)]^[1/2]*3^[1/2]*[-1]^[1/2]) / 2, or a = (2^[1/3] +/- [2^(2/3)]^[1/2]*3^[1/2]*[-1]^[1/2]) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- 2^[(2/3)*(1/2)]*3^[1/2]*i) / 2, or a = (2^[1/3] +/- 2^[(2/3)*(1/2)]*3^[1/2]*i) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = (-2^[1/3] +/- 2^[1/3]*3^[1/2]*i) / 2, or a = (2^[1/3] +/- 2^[1/3]*3^[1/2]*i) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = 2^(1/3)*(-1 +/- 3^[1/2]*i) / 2, or a = 2^(1/3)*(1 +/- 3^[1/2]*i) / 2 a = 2^(1/3), or a = - 2^(1/3), or a = 2^(1/3)*(-1 +/- 3^[1/2]*i) / 2^(3/3), or a = 2^(1/3)*(1 +/- 3^[1/2]*i) / 2^(3/3) a = 2^(1/3), or a = - 2^(1/3), or a = 2^([1/3]-[3/3])*(-1 +/- 3^[1/2]*i), or a = 2^([1/3]-[3/3])*(1 +/- 3^[1/2]*i) a = 2^(1/3), or a = - 2^(1/3), or a = 2^(-2/3)*(-1 +/- 3^[1/2]*i), or a = 2^(-2/3)*(1 +/- 3^[1/2]*i) a = 2^(1/3), or a = -2^(1/3), or a = 2^(-2/3)*(-1 + 3^[1/2]*i), or a = 2^(-2/3)*(-1 - 3^[1/2]*i), or a = 2^(-2/3)*(1 + 3^[1/2]*i), or a = 2^(-2/3)*(1 - 3^[1/2]*i) a = 2^(1/3), or a = -2^(1/3), or a = -2^(-2/3)*(1 - 3^[1/2]*i), or a = -2^(-2/3)*(1 + 3^[1/2]*i), or a = 2^(-2/3)*(1 + 3^[1/2]*i), or a = 2^(-2/3)*(1 - 3^[1/2]*i) a1 = 2^(1/3) a2 = -2^(1/3) a3 = -2^(-2/3)*(1 - 3^[1/2]*i) a4 = -2^(-2/3)*(1 + 3^[1/2]*i) a5 = 2^(-2/3)*(1 + 3^[1/2]*i) a6 = 2^(-2/3)*(1 - 3^[1/2]*i)