Advertisements
Advertisements
Question
If x = `3^(2/3) + 3^(1/3)`, prove that x3 - 9x - 12 = 0
Sum
Advertisements
Solution
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.
shaalaa.com
Solving Exponential Equations
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
Solve for x : (49)x + 4 = 72 x (343)x + 1
Find x, if : `sqrt( 2^( x + 3 )) = 16`
Solve : 4x - 2 - 2x + 1 = 0
Solve : 8 x 22x + 4 x 2x + 1 = 1 + 2x
Evaluate the following:
`(8/27)^((-2)/3) - (1/3)^-2 - 7^0`
Evaluate the following:
`9^(5/2) - 3 xx 5^0 - (1/81)^((-1)/2)`
Solve for x:
`9 xx 3^x = (27)^(2x - 5)`
Solve for x:
`sqrt((8^0 + 2/3)` = (0.6)2-3x
Find the value of k in each of the following:
`(sqrt(9))^-7 xx (sqrt(3))^-5` = 3k
Prove the following:
`(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ (x^"q"/x^"p")^"r"` = 1
