The solution of the equation x 4 + 2 x 3 − 8 x = 16 . The solution of the equation is x = 2 , − 2 , − 1 ± 3 i . Calculation: Consider the provided equation, x 4 + 2 x 3 − 8 x = 16 Convert this equation into the standard form, x 4 + 2 x 3 − 8 x − 16 = 0 Take the common factor out, x 3 x + 2 − 8 x + 2 = 0 x + 2 ( x 3 − 8 ) = 0 x + 2 x − 2 x 2 + 2 x + 4 = 0 Put the first factor equal to zero, x + 2 = 0 x = − 2 Put the second factor equal to zero, x − 2 = 0 x = 2 Put the third factor equal to zero, x 2 + 2 x + 4 = 0 x = − 1 ± 3 i Check: Put x = 2 , − 2 , − 1 ± 3 i in the equation, First put x = 2 2 4 + 2 2 3 − 8 2 = ? 16 16 + 16 − 16 = ? 16 16 = 16 Which is true. Now, put x = − 2 , − 2 4 + 2 − 2 3 − 8 − 2 = ? 16 16 − 16 + 16 = ? 16 16 = 16 Which is true. Hence, the solution of equation is x = 2 , − 2 , − 1 ± 3 i .
The solution of the equation x 4 + 2 x 3 − 8 x = 16 . The solution of the equation is x = 2 , − 2 , − 1 ± 3 i . Calculation: Consider the provided equation, x 4 + 2 x 3 − 8 x = 16 Convert this equation into the standard form, x 4 + 2 x 3 − 8 x − 16 = 0 Take the common factor out, x 3 x + 2 − 8 x + 2 = 0 x + 2 ( x 3 − 8 ) = 0 x + 2 x − 2 x 2 + 2 x + 4 = 0 Put the first factor equal to zero, x + 2 = 0 x = − 2 Put the second factor equal to zero, x − 2 = 0 x = 2 Put the third factor equal to zero, x 2 + 2 x + 4 = 0 x = − 1 ± 3 i Check: Put x = 2 , − 2 , − 1 ± 3 i in the equation, First put x = 2 2 4 + 2 2 3 − 8 2 = ? 16 16 + 16 − 16 = ? 16 16 = 16 Which is true. Now, put x = − 2 , − 2 4 + 2 − 2 3 − 8 − 2 = ? 16 16 − 16 + 16 = ? 16 16 = 16 Which is true. Hence, the solution of equation is x = 2 , − 2 , − 1 ± 3 i .
Solution Summary: The author explains how to calculate the solution of the equation x4+2X3-8x=16.
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