If the A.M.,G.MandH.M between two positive numbers aandb are equal, then
a=b
ab=1
a>b
a<b
Explanation for Correct Option:
Step 1: Apply the formula
AM=(a+b)2
GM=ab
HM=2ab(a+b)
Let a and b be the 2 positive numbers.
Since AM=GM
∴(a+b)2=(ab)
Since AM=HM
∴(a+b)2=2aba+b⇒(a+b)2=4ab
Step 2:Since HM = GM we get
⇒2aba+b=ab
On Squaring the above equation
⇒(a+b)2=4ab
⇒a2+2ab+b2=4ab
⇒a2-2ab+b2=0
⇒(a-b)2=0
∴a=b
Hence option (1) is the answer.