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\(\sqrt{(a+b)}=\sqrt{a}+\sqrt{b} \)  Prove if these equations are true, show your working out 

 

2. \(\sqrt{(a-b)}=\sqrt{a}-\sqrt{b}\)  

 Nov 6, 2017
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√ [ a + b ]  =  √a + √b        square both sides

 

 [√ [ a + b ] ]^2    =  [ √a + √b ]^2

 

a +  b  =    [ √a + √b ]  [ √a + √b ]

 

a + b  =   [√a ]^2   +  2 √a√b  + [√b ]^2

 

a + b  =   a   + 2 √a√b  +  b 

 

If we subtract    a, b from both sides, we have that

 

0  =    2 √a√b

 

This is not true unless a or b  [or both ]  = 0 ....so.....the original equation, in general,  isn't true, either 

 

 

Using similar procedures, the second one will be

 

a  - b  =    a   - 2 √a√b  +  b        subtract a, b from both sides

 

-2b =  -  2√a√b        divide both sides by -2

 

b  =  √a√b     and this is only true if   a = b   and   a,b  ≥ 0

 

So....the second one isn't true, in general, either

 

 

cool cool cool

 Nov 6, 2017
edited by CPhill  Nov 7, 2017

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