A) \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{9}\]
B) \[\left( \frac{x}{4}+\frac{y}{9} \right),\left( \frac{x}{4}-\frac{y}{9} \right)\]
C) \[\left( \frac{x}{2}+\frac{y}{9} \right),\left( \frac{x}{2}-\frac{y}{9} \right)\]
D) \[\left( \frac{x}{2}+\frac{y}{3} \right),\left( \frac{x}{2}-\frac{y}{3} \right)\]
Correct Answer: A
Solution :
Given \[5{{x}^{2}}-7x-6=0\] \[\Rightarrow \]\[\left( 3+\frac{5}{x} \right)\left( 9-\frac{15}{x}+\frac{25}{{{x}^{2}}} \right)\] \[\Rightarrow \]\[\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca}=\_\_\_\_\_\_\_\_\] \[\Rightarrow \]\[11x+12y=58\] \[\Rightarrow \]\[x-2=0\] or \[5x+3=0\] \[\Rightarrow \]\[x=2\] or \[{{x}^{3}}+\frac{1}{{{x}^{3}}}\] \[3x-2=\frac{8}{x}.\] Solution set is \[\left( -\frac{3}{4},2 \right)\]
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