a) Given the equation \( 49X^4y^2 - 14X^2y + 1 = 0 \), prove that: \( y \propto \frac{1}{X^2} \)
Using factorization:
Recognize the equation as a perfect square:
\( (7X^2y - 1)^2 = 0 \)
Therefore:
\( 7X^2y - 1 = 0 \)
\( 7X^2y = 1 \)
\( y = \frac{1}{7X^2} \)
This shows \( y \) is inversely proportional to \( X^2 \), or \( y \propto \frac{1}{X^2} \)
Recognize the equation as a perfect square:
\( (7X^2y - 1)^2 = 0 \)
Therefore:
\( 7X^2y - 1 = 0 \)
\( 7X^2y = 1 \)
\( y = \frac{1}{7X^2} \)
This shows \( y \) is inversely proportional to \( X^2 \), or \( y \propto \frac{1}{X^2} \)
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