Indeed Lengthy

Algebra Level 5

If T n \color{#D61F06}{T_n} denotes the n t h \color{#D61F06}{n^{th}} term of an arithmetic progression such that T p = 1 q \color{#20A900}{T_p\,=\,\frac{1}{q}} and T q = 1 p \color{#20A900}{T_q\,=\,\frac{1}{p}} , then which of the given option is necessarily a root to the equation ( p + 2 q − 3 r ) x 2 + ( q + 2 r − 3 p ) x + ( r + 2 p − 3 q ) = 0 \color{#20A900}{(p+2q-3r)x^{2}\,+\,(q+2r-3p)x\,+\,(r+2p-3q)\,=\,0}

,given that p + 2 q − 3 r ≠ 0 \color{#20A900}{p+2q-3r \neq 0} .

T q \color{#D61F06}{T_{q}} T p \color{#D61F06}{T_p} T p q \color{#D61F06}{T_{pq}} T p + q \color{#D61F06}{T_{p+q}}

Aditya Sky by Aditya Sky , 21, India

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