Fórum de Matemática
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b¹/²+ b-¹/2=11/4

b?

Condição inicial: \(b\geq 0\)

\(b^{1/2}+b^{-1/2}=\frac{11}{4}
b^{1/2}+\frac{1}{b^{1/2}}=\frac{11}{4}
\frac{b+1}{b^{1/2}}=\frac{11}{4}
b^{1/2}=\frac{4(b+1)}{11}
b=\left (\frac{4b+4}{11} \right )^2
b=\frac{16b^2+32b+16}{121}
121b=16b^2+32b+16
-16b^2+89b-16=0
b=\frac{89-11\sqrt{57}}{32}\: \vee \: b=\frac{89+11\sqrt{57}}{32}\: \wedge \: b\geq 0
b=\frac{89-11\sqrt{57}}{32}\: \vee \: b=\frac{89+11\sqrt{57}}{32}\)