Question

Rezolvați aceste ecuatii: va rog!!!!​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

$\it b) Membrul\ st\hat ang\ se\ poate\ scrie:\\ \\ (\underbrace{x+x+x+\ ...\ +x}_{20\ termeni})-(1+2+3+\ ...\ +20)=20x-210\\ \\ Ecua\c{\it t}ia\ devine:\\ \\ 20x-210=0 \Rightarrow 20x=210\Big|_{:10} \Rightarrow 2x=21\Big|_{:2} \Rightarrow x=10,5$

d)

$\it \dfrac{1}{n(n+1)}=\dfrac{1}{n}+\dfrac{1}{n+1}\\ \\ \\ Ecua\c{\it t}ia\ devine:\\ \\ \\ x\Big(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\ ...\ +\dfrac{1}{199}-\dfrac{1}{200}\Big)=398 \Rightarrow\\ \\ \\ \Rightarrow x\Big(\dfrac{1}{1}-\dfrac{1}{200}\Big)=398 \Rightarrow x\cdot\dfrac{199}{200}=398 \Rightarrow x=398\cdot\dfrac{200}{199}=2\cdot200=400$