[administration]

Q. If x= 10/(a+b) and y=10(a+b) and if a,b>0 then x+y is
A) Always less than 10
B) Always greater than or equal to 20
C) always between 10 and 20
D) Always greater than or equal to 30.

[Wonder Boy]

We know that for any value p=/=0 , p+1/p belongs to (-inf, -2] U [2 , inf).

Also for p>0,  p+1/p belongs to  [2 , inf).

Here, since a,b>0 so a+b>0 ,

Now x + y = 10/(a+b) + 10(a+b) = 10[(a+b) + 1/(a+b)]

so x + y >= 10×2 (=20)

Hence Option B) Always greater than or equal to 20 is correct.

 

 

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