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 \[\frac{{{b}^{2}}+{{a}^{2}}}{3}\]
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