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If `a+b+3c=1 and a gt 0, b gt 0, c gt 0`, then the greratest value of `a^(2)b^(2)c^(2)` isA. `(1)/(3^(8))`B. `(1)/(2^(3)3^(8))`C. `(1)/(3^(6)2^(8))`D. `(1)/(2^(10))` |
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Answer» Correct Answer - A If `a+b+3c=1` ……… `((a)/(2)+(a)/(2)+(b)/(2)+(b)/(2)+(3c)/(2)+(3c)/(2))/(6) le ((a^(2))/(2^(2)). (b^(2))/(2^(2)). (3^(2)c^(2))/(2^(2)))^((1)/(6))` `(2^(6))/(6^(6).9)ge a^(2)b^(2)c^(2) implies (1)/(3^(8))ge a^(2)b^(2)c^(2)` `:.` greatest value of `a^(2)b^(2)c^(2)` is `(1)/(3^(8))` |
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