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If `a,b,c in R - {0}` and `a^(2) = bc` and `a + b +c = abc` then the least possible value of `a^(2)` is |
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Answer» Correct Answer - `3` Given `bc = a^(2) …(i)` `b + c = abc - a` `b + c = a^(3) - a…..(ii)` `:.` equation `x^(2) - (b + c)x + bc = 0overset(b)underset(c)(lt)` `x^(2) - (a^(3) - a) x + a^(2) = 0` has two roots `b` and `c`. `b` and `c` are equal so `D ge 0` `(a^(3) - a)^(2) - 4a^(2) ge 0` `a^(2)(a^(4) -2a^(2) - 3) ge 0` `a^(2)(a^(2) - 3)(a^(2) + 1) ge 0` `a^(2) - 3 ge 0` `:. a^(2) ge 3` `:. (a^(2))_(min) = 3` |
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