Question

Arătați ca: (a+b)²+(5a+b)²+(6a+b)²=(2a+b)²+(3a+b)²+(7a+b)²

Answer 1

(a+b)²+(5a+b)²+(6a+b)²=(2a+b)²+(3a+b)²+(7a+b)²;

a²+2ab+b²+25a²+10ab+b²+36a²+12ab+b²=4a²+4ab+b²+9a²+6ab+b²+49a²+14ab+b²;

62a²+24ab+3b²=62a²+24ab+3b² (A);

0=0;

Answer 2

(a + b)^2 + (5a + b)^2 + (6a + b)^2 = a^2 + 2ab + b^2 + 25a^2 + 10ab + b^2 + 36a^2 + 12ab + b^2 = 62a^2 + 24ab + 3b^2

(2a + b)^2 + (3a + b)^2 + (7a + b)^2 = 4a^2 + 4ab + b^2 + 9a^2 + 6ab + b^2 + 49a^2 + 14ab + b^2 = 62a^2 + 24ab + 3b^2

Se observa ca cei doi termeni sunt egali