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(A) Since $a, b, c$ are in $A.P.$,we can write $a = b - d$ and $c = b + d$ for some common difference $d$.Given $abc = 8$,we substitute the terms: $(b

Vedclass · Accepted Answer

$2$

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(A) Since $a, b, c$ are in $A.P.$,we can write $a = b - d$ and $c = b + d$ for some common difference $d$.Given $abc = 8$,we substitute the terms: $(b - d)(b)(b + d) = 8$.This simplifies to $b(b^2 - d^2) = 8$,which implies $b^2 - d^2 = 8/b$.Since $d^2 \ge 0$,we have $b^2 - 8/b = d^2 \ge 0$.This leads to $b^2 \ge 8/b$,or $b^3 \ge 8$.Taking the cube root on both sides,we get $b \ge 2$.Thus,the minimum possible value of $b$ is $2$.

If three positive numbers $a, b$ and $c$ are in $A.P.$ such that $abc = 8$,then the minimum possible value of $b$ is

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