$$ \left(b^{2}+8 ight)^{2}-\left(b^{2}+8 ight)-72=0 $$ The solution set is $$ \{ ilde{\square}\} $$.

Question

$$ \left(b^{2}+8ight)^{2}-\left(b^{2}+8ight)-72=0 $$ The solution set is $$ \{	ilde{\square}\} $$.

UpStudy AI · Accepted Answer

Solve the equation $$ (b^{2}+8)^{2}-(b^{2}+8)-72=0 $$.
Solve the equation by following steps:
- step0: Solve for $$b$$:
  $$\left(b^{2}+8ight)^{2}-\left(b^{2}+8ight)-72=0$$
- step1: Subtract the terms:
  $$\left(b^{2}+8ight)^{2}-b^{2}-80=0$$
- step2: Calculate:
  $$b^{4}+15b^{2}-16=0$$
- step3: Factor the expression:
  $$\left(b-1ight)\left(b+1ight)\left(b^{2}+16ight)=0$$
- step4: Separate into possible cases:
  $$\begin{align}&b-1=0\&b+1=0\&b^{2}+16=0\end{align}$$
- step5: Solve the equation:
  $$\begin{align}&b=1\&b=-1\&b 
otin \mathbb{R}\end{align}$$
- step6: Find the union:
  $$\begin{align}&b=1\&b=-1\end{align}$$
- step7: Rewrite:
  $$b_{1}=-1,b_{2}=1$$
The solution set for the equation $$ (b^{2}+8)^{2}-(b^{2}+8)-72=0 $$ is $$ \{b_{1}=-1,b_{2}=1\} $$.
The solutions are $$ b = -1 $$ and $$ b = 1 $$.

\( \left(b^{2}+8\right)^{2}-\left(b^{2}+8\right)-72=0 \) The solution set is \( \{\tilde{\square}\} \).

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