Question

a) Efectuati calculele:
$( - \frac{1}{4} ) \times ( - \frac{1}{5} ) - ( \sqrt{0.(4)} ) {}^{ - 1} + ( \sqrt{2} - \sqrt{3} ) {}^{2} + \sqrt{24}$
b)Rezolvati in multimea numerelor reale ecuatia:
$\frac{(x - 2) {}^{2} }{2} + x(x - 1) = \frac{3x(x - 5)}{2} + 12$

Answer 1

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Answer 2

$b) \frac{(x - 2) ^{2} }{2} + x(x - 1) = \frac{3x(x - 5)}{2} + 12 \\ \\ (x - 2) ^{2} + 2x(x - 1) = 3x(x - 5) + 24 \\ \\ {x}^{2} - 4x + 4 + 2x - 2x = {3x}^{2} - 15x + 24 \\ \\ {3x}^{2} - 6x + 4 = {3x}^{2} - 15x + 24 \\ \\ - 6x + 4 = - 15x + 24 \\ \\ - 6x = - 15x + 24 - 4 \\ \\ - 6x = - 15x + 20 \\ \\ - 6x + 15 = 20 \\ \\ 9x = 20 \\ \\ x = \frac{20}{9}$