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If a,b,c and d are four positive real numbers such that abcd=1 , what is the minimum value of `(1+a)(1+b)(1+c)(1+d)`.A. 1B. 4C. 16D. 64 |
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Answer» Correct Answer - C `:.(1+a)(1+b)(1+c)(1+d)` ,brgt `=1+a+b+c+d+ab+ac+ad+bc+bd+cd+abc+abd+cda+cdb+abcd " " [" 16 terms "]` `:.AMgeGM` `((1+a)(1+b)(1+c)(1+d))/(16)ge (a^(8)b^(8)c^(8)d^(8))^((1)/(16))` `=(abcd)^((1)/(2))=(1)^((1)/(2))=1 " " [:. Abcd=1]` `((1+a)(1+b)(1+c)(1+d))/(16)ge1` `(1+a)(1+b)(1+c)(1+d)ge16` `:.` Minimum value of `(1+a)(1+b)(1+c)(1+d)` is 16. |
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