practice problems pending

 Q1.


S1.
Cross multiply and simplify to get:
9 (10^3013 - 10^2013) > 0
H.P.

Q2.


S2.
Consider only 'a' side.
Call it A.
1/A = 1 + a^n/(1 + a + .. a^(n-1)) = 1 + 1/[1/a + 1/a^2 ... 1/a^(n)]
Assume
1/A > 1/B
We will figure out whether it's true.
=> 
1/[1/a + .. 1/a^n] > 1/[1/b + .. 1/b^n]
=> 
[1/b + .. 1/b^n] > [1/a + .. 1/a^n]
This is clearly true since a > b.
So the original assumption was correct.
=> 1/A > 1/B
=> A < B.

Q3.
a,b,c are real numbers s.t. a >= b >= c.
Prove or disprove:
a^2 + ac + c^2 >= 3b(a-b+c)

S3.
Make it a quadratic in b by moving RHS to LHS.
And then show D <= 0
So it will be always >= 0
So it will be proved(not disproved).

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