Question

Daca x+1/x=7, atunci x²+1/x²=?

Answer 1

$x+ \frac{1}{x}=7 \\ \\ \Big(x+ \frac{1}{x} \Big)^2 =7^2 \\ \\x ^2 +2 \cdot x \cdot \frac{1}{x}+ \frac{1}{x^2}=49 \\ \\ x^2+ 2+\frac{1}{x^2} =49 \\ \\ x^2+ \frac{1}{x^2}=49-2 \\ \\ \boxed{x^2+ \frac{1}{x^2}=47 }$