Respuesta :

Snor1ax

Answer: u = -10 + i or u = -10 - i

Step-by-step explanation:

[tex]\begin{aligned}&u^{2}+20 u+101=0 \\&u^{2}+10^{2}+2 \times 10 \times 6 u+101-1000=0 \\&(u+10)^{2}=-1\end{aligned}[/tex]

[tex]\begin{aligned}&u+10=\pm \sqrt{-1} \\&u+10=\pm i \\&u=-10 \pm i \\&\bold{u=-10+i \quad \text { or } u=-10-i}\end{aligned}[/tex]

Hrishii

Answer:

[tex]u = - 10 + i, \: \: - (10 + i)[/tex]

Step-by-step explanation:

[tex] {u}^{2} + 20u + 101 = 0 \\ \\ \implies \: {u}^{2} + 20u + 100 + 1 = 0 \\ \\ \implies \: {u}^{2} + 20u + {(10)}^{2} + 1 = 0 \\ \\ \implies \: {(u + 10)}^{2} = - 1 \\ \\ \implies \: {u + 10} = \pm\sqrt{ - 1} \\ \\ \implies \: {u} = \pm \: i - 10\\ \\ u = i - 10 \: \: or \: \: u = - i - 10 \\ \\ u = i - 10 \: \: or \: \: u = - (10 + i) \\ \\ u = - 10 + i, \: \: - (10 + i)[/tex]

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