Salut,
103² = (100 + 3)² = 100² + 2·100·3 + 3² = 10000 + 600 + 9 = 10609.
43·37 = (40 + 3)(40 -- 3) = 40² -- 3² = 1600 -- 9 = 1591.
[tex]\left(x+\dfrac{1}x\right)^2=x^2+2\cdot\dfrac{1}x+\dfrac{1}{x^2}=x^2+2+\dfrac{1}{x^2}.\\\\x^2+\dfrac{1}{x^2}=\left(x+\dfrac{1}x\right)^2-2=5^2-2=25-2=23.\\\\ Deci\ x^2+\dfrac{1}{x^2}=23.[/tex]
