Question

If positive numbers a, b, c, d are in harmonic progression and a #b then​

Answer 1

Step-by-step explanation:

Take a=

p−3q

1

,b=

p−q

1

,c=

p+q

1

,d=

p+3q

1

Then a+d>b+c easily follows

Since (a+d)−(b+c)

=

p

2

−9q

2

2p

−

p

2

−q

2

2p

=2p[

(p

2

−9q

2

)(p

2

−q

2

)

8q

2

]

Which is positive (∵a,b,c,d>0)

Also ad−bc=

p

2

−9q

2

1

−

p

2

−q

2

1

=

(p

2

−9q

2

)(p

2

−q

2

)

8q

2

>0.

Hence, options 'A' and 'D' are correct.

Answer 2

Step-by-step explanation:

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