Question

The value of $(a+b)^3 - (c + d)^3$ is equal to -

• A. $\frac{-128}{3}$
• B. 0
• C. $\frac{-64}{3}$
• D. $\frac{-142}{3}$

Answer 1

Answer: (B)

0

Answer 2

Given the biquadratic equation $81x^4 + 216x^3 + 216x^2 + 96x = 65$, we can rewrite it as $(3x+2)^4 = 81$.

Solving for x, we find the roots: $a = \frac{1}{3}$, $b = -\frac{5}{3}$, $c = -\frac{2}{3} + i$, and $d = -\frac{2}{3} - i$.

Therefore, $a+b = \frac{1}{3} - \frac{5}{3} = -\frac{4}{3}$ and $c+d = -\frac{2}{3} + i -\frac{2}{3} - i = -\frac{4}{3}$.

So, $(a+b)^3 - (c+d)^3 = (-\frac{4}{3})^3 - (-\frac{4}{3})^3 = 0$.