question_answer

Solve the following quadratic equation for x:

\[9{{x}^{2}}-6{{b}^{2}}x-({{a}^{4}}-{{b}^{4}})=0\]

Answer:

We have, \[9{{x}^{2}}-6{{b}^{2}}x-({{a}^{4}}-{{b}^{4}})=0\]

\[(9{{x}^{2}}-6{{b}^{2}}x+{{b}^{4}})-{{a}^{4}}=0\]

\[(3x-{{b}^{2}})-{{({{a}^{2}})}^{2}}=0\]

\[(3x-{{b}^{2}}+{{a}^{2}})(3x-{{b}^{2}}-{{a}^{2}})=0\]

\[x=\frac{{{b}^{2}}-{{a}^{2}}}{3}\]or \[\frac{{{b}^{2}}+{{a}^{2}}}{3}\]