Question

daca x+1suprax=7 ,at x la patrat+1 supra xpatrat=

a.49 b.51 c.47 d.14

expresia (xpatrat-x)(xpatrat-x-6)+9 este patratul numarului .....

(cu rezolvare completa)

Answer 1

1)[tex] \frac{x+1}{x}=7\\ \frac{x}{x} + \frac{1}{x} =7\\ 1+\frac{1}{x}=7\\ (1+\frac{1}{x})^2=7^2\\\\ 1+2\cdot 1 \cdot \frac{1}{x} + \frac{1}{x^2} =49\\ 1+ \frac{1}{x^2} =47\\ 1+ \frac{1}{x^2} =49-2[/tex]
2)Notam:[tex]x^2-x=t\\ (x^2-x)(x^2-x-6)+9=t(t-6)+9=t^2-6t+9=(t-3)^2=\\ =(x^2-x-3)^2[/tex]