How do I find the values of more than one data in a set given the values of harmonic geometric and arithmetic mean i.e
In a study a set of observations were as follows:x,16,20b,4,25,c.Given that the geometric mean is 8.433 the arithmetic mean 11.25 and the harmonic mean 6.026 compute the values x y z
"GM=\\sqrt[6]{x(16)(20y)(4)(25)(z)}=8.433"
"AM=\\dfrac{x+16+20y+4+25+z}{6}=11.25"
"HM=\\dfrac{6}{\\dfrac{1}{x}+\\dfrac{1}{16}+\\dfrac{1}{20y}+\\dfrac{1}{4}+\\dfrac{1}{25}+\\dfrac{1}{z}}=6.026"
"x(20y)z=224.787739"
"x+20y+z=22.5"
"\\dfrac{1}{x}+\\dfrac{1}{20y}+\\dfrac{1}{z}=0.643185"
"x+20y+z=22.5"
"x(20y)+x(z)+20y(z)=144.580101"
Vieta's Theorem
Solve graphically
Answer
"x=2.285, y=0.4083, z=12.049"Or
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