a) Find the solution set for each of the following equations in \( \mathbb{Q} \):
1. \( 2x^2 - 3 = 9 \)
∵ \( 2x^2 - 3 = 9 \)
∴ \( 2x^2 = 9 + 3 = 12 \)
∴ \( x^2 = 12 ÷ 2 = 6 \)
∴ \( x = \pm \sqrt{6} \)
∴ The solution set = \( \left\{ -\sqrt{6}, \sqrt{6} \right\} \)
2. \( 6x^2 - 3 = 4x^2 + 7 \)
∵ \( 6x^2 - 3 = 4x^2 + 7 \)
∴ \( 6x^2 - 4x^2 = 7 + 3 \)
∴ \( 2x^2 = 10 \)
∴ \( x^2 = 10 ÷ 2 = 5 \)
∴ \( x = \pm \sqrt{5} \)
∴ The solution set = \( \left\{ -\sqrt{5}, \sqrt{5} \right\} \)
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