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Use Vieta's formula to calculate the value of an expression
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Two real numbers 𝑠, 𝑡, 𝑠𝑡≠1 satisfy quadratic equations 19𝑠^2+99𝑠+1=0 and 𝑡^2+99𝑡+19=0. Find the value of (𝑠𝑡+4𝑠+1)/𝑡. It can be solved by rewriting one equation and then applying Vieta's Formula.