If three positive numbers a, b and c are in A | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$2$

Vedclass · Answer

(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

Similar Questions

The sum of $p$ terms of an $A.P.$ is $3p^2 + 4p$. Find the $n^{th}$ term.

The sum of the squares of the first $n$ natural numbers exceeds their sum by $330$. Then,$n = $

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an $A.P.$ are $a, b,$ and $c$ respectively,find the value of $a(q-r) + b(r-p) + c(p-q)$.

If the $m^{th}$ term of a $H.P.$ is $n$ and the $n^{th}$ term is $m$,then the $r^{th}$ term will be

The $H.M.$ between the roots of the equation $x^2 - 10x + 11 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module