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sq root problem

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by fangtray » Sat Sep 17, 2011 4:33 am
(root(9 + root(80)) + root(9 - root(80)))^2


please help me solve. sorry i don't know how to make it so you see a sq root sign.
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by knight247 » Sat Sep 17, 2011 4:52 am
[√(9+√80)+√(9-√80)]²

Let √(9+√80)=a so a²=9+√80

Let √(9-√80)=b so b²=(9+√80)

Also a²b²=(9+√80)(9-√80)=9²-80=1
a²b²=1
so ab=1
Substituting the value of a and b in the original question we have

(a+b)²=a²+2ab+b²

Putting the value of a²,b² and ab in the above result we have
9+√80+2(1)+9-√80=9+9+2=20
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