a)
[tex](a + b) {}^{2} + (a - b) {}^{2} = a {}^{2} + 2ab + b {}^{2} + a {}^{2} - 2ab + b {}^{2} = 2(a {}^{2} + b {}^{2} )[/tex]
Or a² + b² = 3 donc
[tex]2(a {}^{2} + b {}^{2} ) = 2 \times 3 = 6[/tex]
b)
[tex]103 {}^{2} = (100 + 3) {}^{2} = 100 {}^{2} + 2 \times 100 \times 3 + 3 {}^{2} = 10000 + 600 + 9 = 10609[/tex]
[tex] {999}^{2} = (1000 - 1) {}^{2} = 1000 {}^{2} - 2 \times 1000 \times 1 + 1 {}^{2} = 1000000 - 2000 + 1 = 998001[/tex]
[tex]75 {}^{2} - 25 {}^{2} = (75 - 25)(75 + 25) = 50 \times 100 = 5000[/tex]
