find two positive numbers whose difference is 12 and whose arithmetic mean exceeds the geometric mean by 2
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find two positive numbers whose difference is 12 and whose arithmetic mean exceeds the geometric mean by 2
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16 and 4
We have,
a−b=12
Am=Gm+2
2a+b=ab+2
(a+b)2=(2ab+4)2
(a−b)2+4ab=4ab+16+16ab
144=16+16ab
9=1+ab
ab=64
b2+12b−64=0
(b+16)(6−4)=0
b=4
Hence,
a=16,b=4
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