The solution of the equation, 3 x 1 3 + 2 x 2 3 = 5 , and check the solution. The solution of the given equation, 3 x 1 3 + 2 x 2 3 = 5 is x = − 125 8 , 1 . Calculation: Consider the provided equation, 3 x 1 3 + 2 x 2 3 = 5 Put x 1 3 = u and convert this equation into quadratic form. 3 u + 2 u 2 = 5 2 u 2 + 3 u − 5 = 0 Now factorize the above equation. 2 u + 5 u − 1 = 0 Put the first factor equal to zero, then replace u with x 1 3 , and solve for x . 2 u + 5 = 0 u = − 5 2 x 1 3 = − 5 2 x = − 125 8 Put the second factor equal to zero, then replace u with x 1 3 , and solve for x . u − 1 = 0 u = 1 x 1 3 = 1 x = 1 Check, Put x = − 125 8 in the given equation, 3 x 1 3 + 2 x 2 3 = 5 3 − 125 8 1 3 + 2 − 125 8 2 3 = ? 5 3 − 5 2 + 2 − 5 2 2 = ? 5 − 15 2 + 25 2 = ? 5 5 = 5 Which is true. Put x = 1 in the given equation, 3 x 1 3 + 2 x 2 3 = 5 . 3 1 1 3 + 2 1 2 3 = ? 5 3 + 2 = ? 5 5 = 5 Which is true. Hence, the solution of the given equation is x = − 125 8 , 1 .
The solution of the equation, 3 x 1 3 + 2 x 2 3 = 5 , and check the solution. The solution of the given equation, 3 x 1 3 + 2 x 2 3 = 5 is x = − 125 8 , 1 . Calculation: Consider the provided equation, 3 x 1 3 + 2 x 2 3 = 5 Put x 1 3 = u and convert this equation into quadratic form. 3 u + 2 u 2 = 5 2 u 2 + 3 u − 5 = 0 Now factorize the above equation. 2 u + 5 u − 1 = 0 Put the first factor equal to zero, then replace u with x 1 3 , and solve for x . 2 u + 5 = 0 u = − 5 2 x 1 3 = − 5 2 x = − 125 8 Put the second factor equal to zero, then replace u with x 1 3 , and solve for x . u − 1 = 0 u = 1 x 1 3 = 1 x = 1 Check, Put x = − 125 8 in the given equation, 3 x 1 3 + 2 x 2 3 = 5 3 − 125 8 1 3 + 2 − 125 8 2 3 = ? 5 3 − 5 2 + 2 − 5 2 2 = ? 5 − 15 2 + 25 2 = ? 5 5 = 5 Which is true. Put x = 1 in the given equation, 3 x 1 3 + 2 x 2 3 = 5 . 3 1 1 3 + 2 1 2 3 = ? 5 3 + 2 = ? 5 5 = 5 Which is true. Hence, the solution of the given equation is x = − 125 8 , 1 .
Solution Summary: The author calculates the solution of the given equation, 3x13+2
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