Which of these statements are true for all a, b > 0? explain your conjecture. (i). 2(a + b) = 2a + 2b (ii) a+b/2= a/2+b/2 (iii) √a+b= √a+√b

Statement (i) , (ii) are TRUE  and

The statement (iii) is FALSE.

Step-by-step explanation:

Given :  a , b are strictly greater than  0.

Now, let us take each statements.

(i) 2(a +b) =  2a + 2b

Yes, the given statement is TRUE, as by DISTRIBUTIVE PROPERTY we get that x (y + z) = xy + xz

(ii)

Yes, the given statement is TRUE, as by DISTRIBUTIVE PROPERTY we get that

(iii

Here, the given statement is FALSE.

Because, if we have a = 2 and b = 3, then

and 2.23 ≠ 3.24

So,

step-by-step explanation:

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