If $a, b, c$ be three unequal positive quantities in $H . P .$ then

a^{100} + c^{100} > 2 b^{100}

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a^{3} + c^{3} > 2 b^{3}

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a^{5} + c^{5} > 2 b^{5}

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a^{2} + c^{2} > 2 b^{2}

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Solution

The correct options are
A $a^{100} + c^{100} > 2 b^{100}$
B $a^{3} + c^{3} > 2 b^{3}$
C $a^{5} + c^{5} > 2 b^{5}$
D $a^{2} + c^{2} > 2 b^{2}$

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Similar questions

a, b, c

a + b + c + d = 0

\frac{a^{5} + b^{5} + c^{5} + d^{5}}{4} = \frac{a^{3} + b^{3} + c^{3} + d^{3}}{3} \cdot \frac{a^{2} + b^{2} + c^{2} + d^{2}}{2}

a

b

a, a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, b

a, b_{1}, b_{2}, b_{3}, b_{4}, b_{5}, b

a, c_{1}, c_{2}, c_{3}, c_{4}, c_{5}, b

a_{3} x^{2} + b_{3} x + c_{3} = 0

If a + b + c = 0

Then prove that

a⁵+ b⁵+ c⁵ a³ + b³+ c³a²+ b²+ c²

------------------- = ---------------------- × --------------------------

5 3 2

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