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

बेरीज

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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पाठ 9: Indices - Exercise 9.1

पाठ 9 Indices
Exercise 9.1 | Q 12

Find x, if : `( sqrt(3/5))^( x + 1) = 125/27`

Solve : `[3^x]^2` : 3x = 9 : 1

Solve : `(sqrt(3))^( x - 3 ) = ( root(4)(3))^( x + 1 )`

Solve for x:

`(81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27`

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If 5^{x + 1} = 25^{x - 2}, find the value of 3^{x - 3} × 2^{3 - x}.

If a^x = b^y = c^z and b² = ac, prove that: y = `[2xz]/[x + z]`

Prove that :
`[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1`

Evaluate the following:

`(2^6 xx 5^-4 xx 3^-3 xx 4^2)/(8^3 xx 15^-3 xx 25^-1)`

If 2^x = 3^y = 12^z ; show that `(1)/z = (1)/y + (2)/x`.