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Cardinality

ntThree unequ...

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ntThree unequal numbers a,b,c are in A.P and a,(b-a),(c-a) are in G .P . prove that , a:b:c=1:3:5n

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a, b, c

are positive and unequal, then prove that:

\frac{b c}{b + c} + \frac{c a}{c + a} + \frac{a b}{a + b} < \frac{1}{2} (a + b + c)

a, b, c

are three unequal numbers such that

a, b, c

A . P .

b - a, c - b, a - c

G . P,

a : b : c

Q. Three unequal numbers

a

b

c

are in Arithmetic Progression and

b - a

c - b

a

are in Geometric Progression.
The value of

\frac{a^{3} + b^{3} + c^{3}}{3 a b c}

a, b, c

G . P

b - c, c - a, a - b

H . P

, then prove that

a + b + c = 3 (a c)^{1 / 2}

Q. If a², b², c²are in AP, prove that a/b+c , b/c+a , c/a+b are in AP

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