Number of real solutions of the equ...
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Number of real solutions of the equation (13 + 2)^2-15x +(13-2)*-5x = 213 is/are

JEE/Engineering Exams
Maths
Solution
127
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( (sqrt{3}+sqrt{2})=frac{1}{sqrt{3}-sqrt{2}} ) ( therefore(sqrt{3}-sqrt{2})^{-left(n^{2}-15 nright)}+(sqrt{3}-sqrt{2})^{n^{2}-15 n}=2 sqrt{3} ) ( Rightarrow frac{1}{(sqrt{3}-52)^{2}-15 n}+(sqrt{2}-sqrt{2})^{2}-15 n ) Let ( frac{1}{(sqrt{3}-2)^{n-15 n}}=t ) ( t+frac{1}{t}=2 sqrt{3} ) ( Rightarrow t^{2}-2 sqrt{3} t+(=0 ) ( left.t=frac{2 sqrt{3} pm sqrt{8}}{2}right)=sqrt{3} pm sqrt{2} ) ( 15 n+n^{2} ) ( (sqrt{3}-52)=(sqrt{3}-sqrt{2}) ) " 4 real solui Thes
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