If the equation \( x^{2}+16 y^{2}-3 x+2=0 \) is satisfied by real v...

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If the equation \( x^{2}+16 y^{2}-3 x+2=0 \) is satisfied by real values of \( x \& y \) then prove
\[
1 \leq x \leq 2 \&-\frac{1}{8} \leq y \leq \frac{1}{8} \text {. }
\]
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