Question
Thu July 26, 2012 By: Nilesh Raikar

True or false with reason if (x-a)(x-b)0 if a and b are any integer such that a>b then a2>b2

Expert Reply
Thu July 26, 2012

1) (x-a)(x-b)<0

(x-a)<0 or (x-b)<0

So, x<a OR x<b

Thus, the given statement is false.

2) if a<0 & b<0 then (a+b)2>0

As the square of any number is always positive.

Thus, the given statement is true.

3) a and b are any integer such that a>b

Squaring both sides,

a2>b2

Thus, the given statement is true.

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