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  • Explain Solution R. D. Sharma Class 12 Chapter deteminants Exercise 5.2 Question 52 sub question 2 maths Textbook Solution.

Explain Solution R. D. Sharma Class 12 Chapter  deteminants Exercise 5.2 Question 52 sub question 2 maths Textbook Solution.

Answers (1)

Answer:x=\frac{-a}{3}

Hint: Use determinant formula

Given: $$ \left|\begin{array}{ccc} x+a & x & x \\ x & x+a & x \\ x & x & x+a \end{array}\right|=0

Solution:

$$ \begin{aligned} &\text { Apply C }_{1} \rightarrow C_{1}+C_{2}+C_{3} \\ &\left|\begin{array}{ccc} 3 x+a & x & x \\ 3 x+a & x+a & x \\ 3 x+a & x & x+a \end{array}\right| \\ &(3 x+a) \text { common from } C_{1} \\ &=(3 x+a)\left|\begin{array}{ccc} 1 & x & x \\ 1 & x+a & x \\ 1 & x & x+c \end{array}\right| \end{aligned}

$$ \begin{aligned} &\text { Apply } \mathrm{R}_{2} \rightarrow R_{2}-R_{1} \& R_{3} \rightarrow R_{3}-R_{1}\\ &=(3 x+a)\left|\begin{array}{ccc} 1 & x & x \\ 0 & a & 0 \\ 0 & 0 & a \end{array}\right|\\ &\text { Expand from } \mathrm{C}_{1}\\ &=(3 x+a) a^{2}=0\\ &3 x+a=0, a^{2}=0\\ &3 x=-a, a=0\\ &x=\frac{-a}{3}, a=0 \end{aligned}

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