(A) 33 x --x at-x as a5 - a - * a? ...
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(A) 33 x --x at-x as a5 - a - * a? - x a? -x a-x a Value of the x

JEE/Engineering Exams
Maths
Solution
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( =left|begin{array}{ccc}a^{3}-x & a^{4}-x & a^{5}-x a^{5}-x & a^{6}-x & a^{7}-x a^{7}-x & a^{8}-x & a^{9}-x a^{3}-x & a^{4}-x & a^{5}-x a^{5}-a^{3} & a^{6}-a^{4} & a^{7}-a^{5} a^{7}-a^{5} & a^{8}-a^{6} & a^{9}-a^{7}end{array}right| quad begin{array}{c}mid x_{12}(-1) mid R_{23}(-1)end{array} ) ( =left|begin{array}{ccc}a^{3}-x & a^{4}-a & a^{5}-x a^{3} & left(a^{2}-1right) & a^{4}left(a^{2}-1right) & a^{5}left(a^{2}-1right) a^{5} & left(a^{2}-1right) & a^{6}left(a^{2}-1right) & a^{7}left(a^{2}-1right)end{array}right| ) ( =left(a^{2}-1right)^{2} times a^{3} times a^{5}left|begin{array}{ccc}a^{3}-a & a^{4}-a c & a^{5}-a 1 & a & a^{2} 1 & a & a^{2}end{array}right| ) ( R_{2}left(frac{1}{a^{3}}right) ; R_{3}left(frac{1}{a^{5}}right) ; R_{2}left(frac{1}{a^{2}-1}right) ; R_{3}left(frac{1}{a^{2}-1}right) ) ( =left(a^{2}-1right)^{2} times a^{8}left|begin{array}{cc}a^{3}-x & a^{4}-x & a^{5}-x 1 & a & a^{2} 0 & 0 & 0end{array}right| R_{23}(-1) ) ( =0 )
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