If x 3 + x = 0 for some real number x , then how many values of x satisfy this equation?
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x 3 + x = 0 x ( x 2 + 1 ) = 0 ⟹ x = 0 , x 2 = − 1 ∴ x = 0 , x = i are solutions to the expression
Here x = 0 is real whereas x = i is imaginary so it have 1 real solution
It's a cubic equation and you have only two solutions!
Actually, there will be three roots x = 0 and x = ± i .You forgot that x = − i is also a root to this equation.
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That won't affect the answer of the question. A cubic root has atmost 3 solutions. I agree − i is also a soln
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x 3 + x x ( x 2 + 1 ) x = 0 x = 0 But for real number x , x 2 ⟹ x 2 ⟹ x = 0 = 0 ( or ) x 2 + 1 = 0 ( or ) x 2 = − 1 ≥ 0 = − 1 = 0
Thus only 1 value satisfies this equation.