If (1/a) + (1/b) + (1/c) = (1/(a + b + c)) then (1/a^3 ) + (1/(b^3 )) + (1/c^3 ) = ?


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 174568 by AgniMath last updated on 04/Aug/22

$If \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{a + b + c} then$ $\frac{1}{a^{3}} + \frac{1}{b^{3}} + \frac{1}{c^{3}} = ?$
	Answered by behi834171 last updated on 04/Aug/22

	$i m p o s s i b l e t o f i n d .$ $b y u s i n g : A M - G M i n i q u a l i t y :$ $[\frac{Σ x_{i}}{3} ⩾ \sqrt[3]{Π x_{i}}]$ $\Rightarrow Σ \frac{1}{a} ⩾ 3 \sqrt[3]{Π \frac{1}{a}} \overset{(Σ \frac{1}{a} = \frac{1}{Σ a})}{\Rightarrow} \frac{1}{Σ a} ⩾ 3 \sqrt[3]{Π \frac{1}{a}} \Rightarrow$ $\Rightarrow Σ a ⩽ \frac{1}{3 \sqrt[3]{Π \frac{1}{a}}} = \frac{1}{3} . \sqrt[3]{Π a}$ $a n d w e k n o w t h a t : [A M - G M i n q .]$ $Σ a ⩾ 3 \sqrt[3]{Π a}$ $i . e : 3 \sqrt[3]{Π a} ⩽ Σ a ⩽ \frac{1}{3} . \sqrt[3]{Π a}$ $a n d t h i s i s i m p o s s i b l e .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum