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Algebra Level 4

If A , G , H A,G,H be respective the A . M , G . M , H . M A.M,G.M,H.M Between two positive numbers and if x A = y G = z H xA=yG=zH where x , y , z x,y,z are non zero positive quantities , then x , y , z x,y,z are in

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G.P A.P H.P A.G.P

Shivam Jadhav by Shivam Jadhav , 22, India

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1 solution

Shivam Jadhav
Apr 5, 2016

x a + b 2 = y a b = z 2 a b a + b x\frac{a+b}{2}=y\sqrt{ab}=z\frac{2ab}{a+b}

a + b 2 a b = y x = z y \frac{a+b}{2\sqrt{ab}}=\frac{y}{x}=\frac{z}{y}

y 2 = x z y^{2}=xz

x , y , z x,y,z are in G.P

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