If ab^2 + bc^2 + ca^2 = 0 then find ((a/b) + (b/c)) + ((b/c) + (c/a)) + ((c/a) + (a/b)) + 2.


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 216312 by MATHEMATICSAM last updated on 03/Feb/25

$If {a b}^{2} + {b c}^{2} + {c a}^{2} = 0 then find$ $(\frac{a}{b} + \frac{b}{c}) + (\frac{b}{c} + \frac{c}{a}) + (\frac{c}{a} + \frac{a}{b}) + 2 .$
	Answered by Rasheed.Sindhi last updated on 03/Feb/25

	${a b}^{2} + {b c}^{2} + {c a}^{2} = 0$ $\frac{{a b}^{2}}{a b c} + \frac{{b c}^{2}}{a b c} + \frac{{c a}^{2}}{a b c} = 0$ $\frac{b}{c} + \frac{c}{a} + \frac{a}{b} = 0$ $2 (\frac{b}{c} + \frac{c}{a} + \frac{a}{b}) = 0$ $\frac{b}{c} + \frac{c}{a} + \frac{a}{b} + \frac{b}{c} + \frac{c}{a} + \frac{a}{b} = 0$ $(\frac{a}{b} + \frac{b}{c}) + (\frac{b}{c} + \frac{c}{a}) + (\frac{c}{a} + \frac{a}{b}) + 2 = 2$
	Answered by som(math1967) last updated on 03/Feb/25

	$\frac{2 a}{b} + \frac{2 b}{c} + \frac{2 c}{a} + 2$ $= \frac{2 a^{2} c + 2 b^{2} a + 2 c^{2} b}{a b c} + 2$ $= \frac{2 ({a b}^{2} + {b c}^{2} + {c a}^{2})}{a b c} + 2$ $= \frac{2 \times 0}{a b c} + 2 = 2$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum