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if x be one A.M and y,z be two G.M’s between any two positive numbers show that y3 + z3 = 2xyz
Hint: Let two numbers be a and b, then x =(a+b)/2. and y = sqrt(az) , z = sqrt(yb). Put this values of x,y and z in the LHS and RHS. On simplification you can easily prove LHS = RHS. Thanks.
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