Advertisements
Advertisements
Question
If x = `3^(2/3) + 3^(1/3)`, prove that x3 - 9x - 12 = 0
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.
APPEARS IN
RELATED QUESTIONS
Solve for x : 9x+2 = 720 + 9x
Solve for x: `4^(x-1) × (0.5)^(3 - 2x) = (1/8)^-x`
Prove that : `((x^a)/(x^b))^( a + b - c ) (( x^b)/(x^c))^( b + c - a )((x^c)/(x^a))^( c + a - b)`
If `((a^-1b^2 )/(a^2b^-4))^7 ÷ (( a^3b^-5)/(a^-2b^3))^-5 = a^x . b^y` , find x + y.
If 3x + 1 = 9x - 3 , find the value of 21 + x.
Evaluate the following:
`(2^6 xx 5^-4 xx 3^-3 xx 4^2)/(8^3 xx 15^-3 xx 25^-1)`
Evaluate the following:
`(1 - 15/64)^(-1/2)`
Solve for x:
1 = px
Find the value of k in each of the following:
`root(4)root(3)(x^2)` = xk
Prove the following:
`root("ab")(x^"a"/x^"b")·root("bc")(x^"b"/x^"c")·root("ca")(x^"c"/x^"a")` = 1
