Given that:
3√3
x= --------------
1+ 3√3 + 3√9
Find the value of:
4x3 + 9x+1
------------
8x3 + 18x-1
Make the cube root of three a parameter.
Let c = ∛3 or c^3 = 3
x = c/(1+c+c^2) = c(c-1)/(c^3 - 1) = c(c-1)/2
x^3 = c^3(c-1)^3 / 8 = (3/8)(c-1)^3
after multiplying top and bottom by 2 to get rid of fractions:
Numerator = 3(c-1)^3 + 9c(c-1) + 2
3c^3 - 9c^2 + 9c - 3 + 9c^2 - 9c + 2
= 3c^3 - 1 = 8
Denominator = 6(c-1)^3 + 18c(c-1) - 2
6c^3 - 18c^2 + 18c - 6 + 18c^2 - 18c - 2
= 6c^3 - 8 = 10
Answer: 4/5
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Posted by Larry
on 2024-10-18 11:59:03 |
Solution