Given B & sup2; + C & sup2; = 2A & sup2; - 3A + 7 BC = A & sup2; - 2a-7, find the value range of A | Math enthusiast | Mathematical art

Given B & sup2; + C & sup2; = 2A & sup2; - 3A + 7 BC = A & sup2; - 2a-7, find the value range of A

(b+c)²>=0
b²+c²+2bc=2a²-3a+7+2a²-4a-14>=0
4a²-5a-7>=0
a=(5+√137)/8
b²+c²>=0
2A & sup2; - 3A + 7 > = 0, constant holds
So a = (5 + √ 137) / 8

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