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# Grotesque

Consider the following system of equations:

$a = (\tfrac{15b}{c} + 5d - 1)^{0.5} , \; b = (\tfrac{15c}{d} + 5a - 1)^{0.5}$ $c = (\tfrac{15d}{a} + 5b -1 )^{0.5}, \; d =(\tfrac{15a}{b} + 5c - 1)^{0.5}$

Evaluate the value(s) of the expression

$\dfrac{abc+abd+acd+bcd+4abcd}{a+b+c+d+ab+ac+ad+bc+bd+cd.}$

Note by Guilherme Dela Corte
3 years, 6 months ago

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Hint: if we let $$a=b=c=d$$, we yield $$a=7$$, and the desired expression has only one possible value: $$\boxed{14.}$$

- 3 years, 1 month ago

You can't just assume that the expression is constant $$\forall a,b,c,d\in\mathbb R$$; you'll have to prove it.

- 3 years, 1 month ago