X^3 +8=9x^(3/2)?

To solve this equation, we can first rewrite it as:

x^3 - 9x^(3/2) + 8 = 0

Now, let's make a substitution to simplify the equation. Let's set y = x^(3/2).

Now, the equation becomes:

y^2 - 9y + 8 = 0

This is a quadratic equation that can be factored as:

(y - 1)(y - 8) = 0

Setting each factor to zero gives us:

y - 1 = 0 or y - 8 = 0

y = 1 or y = 8

Now, substitute back in the original substitution:

x^(3/2) = 1 or x^(3/2) = 8

Taking the square root of both sides gives us:

x = 1^(2/3) or x = 8^(2/3)

x = 1 or x = 4

Therefore, the solutions to the equation x^3 + 8 = 9x^(3/2) are x = 1 and x = 4.

X=1&4