[tex](6+ \frac{1}{3} x) + (-\frac{1}{3} x +6) + (\frac{1}{3} x - 4)^{2} = 4[/tex]
[tex]6+ \frac{1}{3} x -\frac{1}{3} x +6 + (\frac{1}{3} x - 4)^{2} = 4[/tex]
(stosujemy wzór skróconego mnożenia)
[tex]6+ \frac{1}{3} x -\frac{1}{3} x +6 + \frac{1}{9}x^{2} - \frac{8}{3}x + 16 = 4[/tex]
[tex]\frac{1}{9} x^{2} - \frac{8}{3}x + 24 = 0[/tex]
(wyliczamy deltę ze wzoru: Δ [tex]= b^{2} - 4ac[/tex])
[tex](-\frac{8}{3})^{2} - 4 * \frac{1}{9} * 24 = - \frac{32}{9}[/tex]
Δ [tex]< 0[/tex] (brak pierwiastków)
- Odpowiedź: [tex]x[/tex] ∉ [tex]R[/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
[tex](-4x - 3)(4x -3) + 8(1 - \sqrt{2} x)^{2} = 1[/tex]
[tex]-16x^{2} + 12x - 12x + 9 + 8(1 - \sqrt{2} x)^{2} = 1[/tex]
[tex]- 16x^{2} + 9 + 8(1 - 2\sqrt{2} x + 2x^{2} ) = 1[/tex]
[tex]-16x^{2} + 9 + 8 - 16\sqrt{2} x + 16x^{2} - 1 = 0[/tex]
[tex]- 16\sqrt{2} x + 16 = 0 \\- 16\sqrt{2} x = -16 |^{2} \\ 512x^{2} = 256 \\x^{2} = \frac{256}{512} \\ x^{2} = \frac{1}{2}\\x = \sqrt\frac{1}{2}[/tex][tex]x = \frac{\sqrt{2} }{2}[/tex]
- Odpowiedź: [tex]x = \frac{\sqrt{2} }{2}[/tex]
