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Oblicz 3(x+2)²/4-x²=6-x²/4 |*4
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Odpowiedź :

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Odpowiedź:

[tex] \frac{3 {(x + 2)}^{2} }{4} = \frac{6 - {x}^{2} }{4} \times 4 \\ \frac{3 {(x + 2)}^{2} }{4} = 6 - {x}^{2} \\ \frac{3( {x}^{2} + 4x + 4)}{4} = 6 - {x}^{2} \\ \frac{3 {x}^{2} + 12x + 12 }{4} = 6 - {x}^{2} \\ 3 {x}^{2} + 12 + 12 = 24 - 4 {x}^{2} \\ 7 {x}^{2} + 12x - 12 = 0 \\ \\ \\ \\ x1 = \frac{ - 12 + \sqrt{ {12}^{2} - 4 \times 7 \times ( - 12)} }{2 \times 7 } \\ x2 = \frac{ - 12 - \sqrt{ {12}^{2} - 4 \times 7 \times ( - 12) } }{2 \times 7} \\ x1 = - \frac{ - 12 + 4 \sqrt{30} }{14} \\ x2 = \frac{ - 12 - 4 \sqrt{30} }{14} \\ x1 = \frac{ - 6 + 2 \sqrt{30} }{7} \\ x2 = \frac{ - 6 - 2 \sqrt{30} }{7} [/tex]