Question

Rezolvati ecuatia in C?

Answer 1

(x² - 3x)² + 3(x² - 3x) - 28 = 0

Notam x² - 3x = t

t² + 3t - 28 = 0

Δ = 9 - 4*(-28)

Δ = 9 + 112

Δ = 121 = 11²

↓

$t_{1} = \frac{-3-\sqrt{121}}{2} \\ \\ t_{1} = \frac{-3-11}{2}\\ \\ t_{1} =-7$

$t_{2} =\frac{-3+\sqrt{121}}{2}\\ \\ t_{2}=\frac{-3+11}{2} \\ \\ t_{2}=4$

Pentru t = -7 → x²-3x = -7

→ x² - 3x + 7 = 0

Δ =9-28

Δ = -19 = (√19i)²

 $x_{1}=\frac{3-i\sqrt{-(19i)^{2}}}{2\\} \\\\ x_{1}=\frac{3-i\sqrt{19}}{2}$

$x_{2}=\frac{3+i\sqrt{-(19i)^{2}}}{2\\} \\\\ x_{2}=\frac{3+i\sqrt{19}}{2}$

Pentru t = 4 → x²-3x = 4
x²-3x-4 = 0
Δ = 9+16
Δ = 25 
$x_{1} = \frac{3-5}{2} =-1$
$x_{2}= \frac{3+5}{2}=4$