Question

A^2(64a^2-3)/3=27-4a^2/4

Answer 1

The answer is a = 3/4 = 0.75

First get rid of the paranthesis,

`{a}^(2) (64 {a}^(2) - 3) = 64 {a}^(4) - 3 {a}^(2)`
Then set the denominators equal:

`\frac{ 256 {a}^(4) - 12 {a}^(2)}{12} = \frac{81 - 12 {a}^(2) }{12}`
Then remove the denominators and solve:

`256 {a}^(4) - 12 {a}^(2) = 81 - 12 {a}^(2)`
Eliminate -12a^2 by adding 12a^2 to both sides:

`256 {a}^(4) = 81`
Take the fourth root of them or take the square root twice:

`\sqrt[4]{256 {a}^(4) } = \sqrt[4]{81} \\ 4a = 3`
Divide both sides by 4:

`a = (3)/(4) = 0.75`