💥 Q 07 Prep 2 Question Bank T1

a) Find the solution set for each of the following equations in Q and R:

1. \( \frac{3}{4}x^2 = \frac{9}{2} \)

∵ \( \frac{3}{4}x^2 = \frac{9}{2} \)

∴ \( x^2 = \frac{9}{2} \times \frac{4}{3} = 6 \)

∴ \( x = \pm \sqrt{6} \)

∴ The solution set in \( \mathbb{Q} = \left\{ -\sqrt{6}, \sqrt{6} \right\} \)

∴ The solution set in \( \mathbb{R} = \left\{ -\sqrt{6}, \sqrt{6} \right\} \)

2. \( 2(x^2 - 1) = -10 \)

∵ \( 2(x^2 - 1) = -10 \)

∴ \( x^2 - 1 = -10 \div 2 = -5 \)

∴ \( x^2 = -5 + 1 = -4 \)

∴ \( x = \pm \sqrt{-4} \)

∴ The solution set in \( \mathbb{Q} = \emptyset \)

∴ The solution set in \( \mathbb{R} = \emptyset \)

MR/Nasef.N

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