Question

$Find \: all \: (a,b,c) \in \R^3 \: satisfying \: the \\ \rm following \: system \: of \: equations$
$\footnotesize \displaystyle \begin{cases} \displaystyle \rm {a}^{2} = \frac{ {b}^{3} + 9 \sqrt{3} }{3b} = \frac{ {c}^3 + 16 }{3c} \\ \\ \rm {b}^{2} = \dfrac{ {a}^{3} - 10 }{3a} = \dfrac{ {c}^{3} + 28 }{3c} \\ \\ \rm {c}^{2} = \dfrac{ {b}^3 + 45 \sqrt{3} }{3b} = \dfrac{ {a}^{3} - 88}{3a} \end{cases}$
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Answer 1

Step-by-step explanation:

Given, a+2b+3b=4

or, (ai+bj+ck).(i+2j+3k)=4

Now taking modulus both sides we get,

a2+b2+c2.12+22+32=4

or, a2+b2+c2=144

or, a2+b2+c2=1416=78=1+71.

So least value (to the nearest integer) of (a2+b2+c2) is 1.

Answer 2

Answer:

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