If X = 3 2 3 + 3 1 3 , Prove that X3 - 9x - 12 = 0 - Mathematics

If x = `3^(2/3) + 3^(1/3)`, prove that x³ - 9x - 12 = 0

Sum

x = `3^(2/3) + 3^(1/3)`

⇒ x³ = `3^2 + 3 + 3 xx 3^(2/3) xx 3^(1/3)(3^(2/3) + 3^(1/3))`

⇒ x³ = `9 + 3 + 3 xx 3^(2/3 + 1/3)(x)`
⇒ x³ = 12 + 9x
⇒ x³ - 9x - 12 = 0.

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Solving Exponential Equations

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 12

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