Question

Dacă 1 supra 2 plus 1 supra 3 plus 1 supra n egal cu 1 atunci n egal cu...​

Answer 1

Răspuns:

    n = 6

Explicație pas cu pas:

    $\frac{1}{2}+\frac{1}{3}+\frac{1}{n}=1$

    n ≠ 0

    $\frac{3}{6}+\frac{2}{6}+\frac{1}{n}=1$

    $\frac{5}{6}+\frac{1}{n}=\frac{1}{1}$

    $\frac{1}{n}=\frac{6}{6}-\frac{5}{6}$

    $\frac{1}{n}=\frac{1}{6}$

    $n = \frac{1*6}{1}$

    $n = 6$

Answer 2

$\dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{n}}} = 1\\ \\ \\\Rightarrow \dfrac{1}{2+\dfrac{1}{\dfrac{3n+1}{n}}} = 1 \Rightarrow \dfrac{1}{2+\dfrac{n}{3n+1}} = 1\\ \\ \\ \Rightarrow \dfrac{1}{\dfrac{6n+2+n}{3n+1}} = 1 \Rightarrow \dfrac{3n+1}{7n+2} = 1\\ \\ \\ \Rightarrow 3n+1 = 7n+2 \Rightarrow 7n-3n = 1-2\Rightarrow 4n = -1\\ \\ \\ \Rightarrow \boxed{n =-\dfrac{1}{4}}$