If a- b- c be three real numbers of the same sign then the value of a-b - b-c - c-a lies in the interval

Since a, b, c are of same sign, a/b, b/c, c/a are all +ive. Apply A.M. ≥ G.M. ∴ E ≥ 3 [ a/b.b/c.c/a ]^1/3=3 therefore E lies in the interval [3, ∞) ...

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Byju's Answer

Standard XIII

Mathematics

Properties of Inequalities

If a, b, c be...

Question

If a, b, c be three real numbers of the same sign then the value of $\frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ lies in the interval

[3, \infty)

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(3, \infty)

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[2, \infty)

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(- \infty, 3)

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Solution

The correct option is A $[3, \infty)$
Since a, b, c are of same sign, $\frac{a}{b}, \frac{b}{c}, \frac{c}{a}$ are all +ive.
Apply A.M. $\geq$ G.M.
$∴ E \geq 3 {[\frac{a}{b} . \frac{b}{c} . \frac{c}{a}]}^{\frac{1}{3}} = 3$
therefore E lies in the interval $[3, \infty)$

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If a, b, c be three real numbers of the same sign then the value of ab+bc+ca lies in the interval

The correct option is A [3,∞)Since a, b, c are of same sign, ab,bc,ca are all +ive. Apply A.M. ≥ G.M. ∴E≥3[ab.bc.ca]13=3 therefore E lies in the interval [3,∞)

If a, b, c be three real numbers of the same sign then the value of $\frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ lies in the interval

The correct option is A $[3, \infty)$
Since a, b, c are of same sign, $\frac{a}{b}, \frac{b}{c}, \frac{c}{a}$ are all +ive.
Apply A.M. $\geq$ G.M.
$∴ E \geq 3 {[\frac{a}{b} . \frac{b}{c} . \frac{c}{a}]}^{\frac{1}{3}} = 3$
therefore E lies in the interval $[3, \infty)$