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  • Explain Solution R.D. Sharma Class 12 Chapter deteminants Exercise 5.2 Question 52 Sub Question 10 maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter  deteminants Exercise 5.2 Question 52 Sub Question 10 maths Textbook Solution.

Answers (1)

Answer: x=-12,0

Hint: Use determinant formula

Given: \left|\begin{array}{lll} 4-x & 4+x & 4+x \\ 4+x & 4-x & 4+x \\ 4+x & 4+x & 4-x \end{array}\right|=0

Solution:

\begin{aligned} &\text { Apply C }_{1} \rightarrow C_{1}+C_{2}+C_{3} \\ &\left|\begin{array}{lll} 12+x & 4+x & 4+x \\ 12+x & 4-x & 4+x \\ 12+x & 4+x & 4-x \end{array}\right|=0 \end{aligned}

\begin{aligned} &(12+x) \text { common from } \mathrm{C}_{1}\\ &(12+x)\left|\begin{array}{ccc} 1 & 4+x & 4+x \\ 1 & 4-x & 4+x \\ 1 & 4+x & 4-x \end{array}\right|=0 \end{aligned}

\begin{aligned} &\text { Apply } \mathrm{R}_{2} \rightarrow R_{2}-R_{1} \& R_{3} \rightarrow R_{3}-R_{1}\\ &(12+x)\left|\begin{array}{ccc} 1 & 4+x & 4+x \\ 0 & -2 x & 0 \\ 0 & 0 & -2 x \end{array}\right|=0\\ &\text { Expand from } \mathrm{C}_{1}\\ &(12+x)\left(4 x^{2}\right)=0\\ &12+x=0,4 x^{2}=0\\ &x=-12, x=0 \end{aligned}

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