AM and GM of two postive real numbers a and b are equal if and only if
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Answer:
Step-by-step explanation:
] AM=
2
a+b
GM=
ab
HM=
a+b
2ab
AM = GM AM = HM
2
(a+b)
=
ab
2
a+b
=
a+b
2ab
= (a+b)
2
=4ab=(a+b)
2
=4ab
HM = GM
a+b
2ab
=
ab
= 4ab=(a+b)
2
= a
2
+b
2
+2ab=4ab
= a
2
+b
2
−2ab=0
= (a−b)
2
=0
∴a=b
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