Question

Dam naj! Rozwiąż równanie
√36-12x+x^2=2
(Odp: x=4, x=8)​

Answer 1

Verified answer

Odpowiedź:

√36-12x+x² = 2     /^²

36 -12x + x² = 4    /-4

x² -12x + 32 = 0

Δ = b² - 4ac      

w naszym równaniu: b = -12   a = 1   c = 32

Δ = (-12)² - 4·1·32 = 144 - 128 = 16

√Δ = √16 = 4

x₁ = [tex]\frac{-b - \sqrt{delta} }{2a}[/tex] = [tex]\frac{12 - 4 }{2\\}[/tex] = 4

x₂ = [tex]\frac{-b + \sqrt{delta} }{2a}[/tex] = [tex]\frac{12 + 4 }{2\\}[/tex] = 8

Answer 2

Odpowiedź:

[tex]\displaystyle\sqrt{36-12x+x^{2} } =2\\\sqrt{(x-6)^2} =2\\|x-6|=2 \quad \Rightarrow x-6=2\quad \lor x-6=-2\\x=8\quad \lor x=4[/tex]