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Solve - 35 x...

Question

Solve -
$35 x^{2} - 12 a x + (a^{2} - b^{2}) = 0$

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Solution

given,

$35 x^{2} - 12 a x + (a^{2} - b^{2}) = 0$

$35 x^{2} - 12 a x + a^{2} - b^{2} = 0$

$a = 35, b = - 12 a, c = a^{2} - b^{2}$

$x = \frac{- (- 12 a) \pm \sqrt{{(- 12 a)}^{2} - 4 \cdot 35 (a^{2} - b^{2})}}{2 \times 35}$

$x = \frac{2 (6 a + \sqrt{a^{2} + b^{2} \cdot 35})}{70}$

$∴ x = \frac{6 a \pm \sqrt{a^{2} + 35 b^{2}}}{35}$

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