QJEEM20Ma1df7: JEE Main 2020 Mathematics - Class 12 JEEM20Ma1df7 Solution: If the system of linear equations 2x + 2ay + az = 0 2x + 3by +…

Question

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If the system of linear equations
2x + 2ay + az = 0
2x + 3by + bz = 0
2x + 4cy + cz = 0,
where a, b, c

\in

R are non-zero distinct; has a non-zero solution, then:

Accepted Answer

For non-zero solution

| \begin{matrix} 2 & 2 a & a \\ 2 & 3 b & b \\ 2 & 4 c & c \end{matrix} | = 0

\Rightarrow

| \begin{matrix} 1 & 2 a & a \\ 0 & 3 b - 2 a & b - a \\ 0 & 4 c - 2 a & c - a \end{matrix} | = 0

\Rightarrow

(3b – 2a) (c –a) – (b – a) (4c – 2a) = 0

\Rightarrow

2ac = bc + ab

\Rightarrow

\frac{2}{b} = \frac{1}{a} + \frac{1}{c}

∴

\frac{1}{a}, \frac{1}{b}, \frac{1}{c}

are in A.P.

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