A=√(6-√11)andB=√(6+√11) then find A+B
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We have A=√(6-√11), B=√(6+√11).
To find A+B, we should use perfect square identity.
The example is (A+B)²=A²+B²+2AB.
A²=6-√11
B²=6+√11
AB=√(6-√11)(6+√11), or AB=5
A²+B² is 12, 2AB is 10.
Their sum is 24. Therefore, (A+B)²=24.
We know that A>0, B>0. Therefore, A+B>0.
We can observe that A+B is positive root of 24.
Therefore, A+B=2√6.
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