Question

solve for X
$pqx {}^{2} - (p { }^{2} | + q {}^{2} )x + pq = 0$
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Answer 1

Answer:

$\boxed{\mathbf{x = \frac{p}{q} \: \: or \: \: \frac{q}{p} }}$

Step-by-step explanation:

Given equation,

$\mathbf{pqx {}^{2} - (p {}^{2} + q {}^{2}) + pq = 0 }$

By splitting the middle term,

$\mathbf{pqx {}^{2} - px^{2} - qx{}^{2} + pq = 0 } \\ \\ \mathbf{ \implies \: px(qx - p) - q(qx - p) = 0} \\ \\ \mathbf{ \implies \: (px - q)(qx - p) = 0} \\ \\ \mathbf{ \implies \:px - q = 0 \: \: or \: \: qx - p = 0 } \\ \\ \ \implies \: \boxed{ \mathbf{x = \frac{q}{p} \: \: or \: \: \frac{p}{q} }}$

The zeros of the given quadratic equation are p/q and q/p.