Question

Let a, b, and c be positive numbers satisfying

a^2*b = 1
b^2*c = 2
c^2*a = 3

Find a.

Answer 1

Hi,

a=0.9685407954....=
`\sqrt[9]{(3)/(4) }`

Explanation:

`a^2*b=1 \Longrightarrow\ b=(1)/(a^2) \\\\b^2*c=2\Longrightarrow\ (c)/(a^4)=2\Longrightarrow\ c=2*a^4\Longrightarrow\ c^2=4*a^8 \\c^2*a=3\Longrightarrow\ 4*a^8*a=3 \Longrightarrow\ a^9=(3)/(4) \Longrightarrow\ a=\sqrt[9]{(3)/(4)} \approx{0.97}`