Persamaan kuadrat x²-6x+3=0 mempunyai akar-akar x1 dan x2 maka nilai dari x2.x1³ - x1.x2³=

[tex] {(x - 3)}^{2} - 9 + 3 = 0 \\ x - 3 = + - \sqrt{6} \\ x1 = 3 + \sqrt{6} \\ x2 = 3 - \sqrt{6} \\ x1 + x2 = 6 \\x1 - x2 = 2 \sqrt{6} \\ x1.x2 = 3 \\{x1}^{3} x2 - {x2}^{3} x1 = {x1}^{2} x1x2 - {x2}^{2} x2x1 = x1x2( {x1}^{2} - {x2}^{2} ) = \\ x1x2(x1 + x2)(x1 - x2) = 3(6)(2 \sqrt{6} ) = 36 \sqrt{6} [/tex]