CUET · MATHS · PYQ PAPER 2023
One root of the equation \(\left|\begin{array}{ccc}3 x-8 & 3 & 3 \\ 3 & 3 x-8 & 3 \\ 3 & 3 & 3 x-8\end{array}\right|=0\) is:
- A \(\frac{8}{3}\)
- B \(\frac{2}{3}\)
- C \(\frac{1}{3}\)
- D \(\frac{16}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
\( \left|\begin{array}{ccc}a & b & b \\ b & a & b \\ b & b & a\end{array}\right| = (a+2b)(a-b)^2 \) \( a = 3x-8, b = 3 \) \( ((3x-8)+2(3))((3x-8)-3)^2 = 0 \) \( (3x-2)(3x-11)^2 = 0 \) \( 3x-2=0 \) \( x=\frac{2}{3} \)
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