Вправи: 921

921. Розв’яжи рівняння.

a) xx+3 – xx-3 = 4; xx-3+ x(x+3)x+3(x-3) = 4; x2-3x+x2+3x x2-9 = 4;

2x2x2-9 = 4, x ≠ ± 3; 2x² = 4x² – 36; 2x² = 36; x² = 18; x = ± 18;

б) x+2x-2 + x-2x+2 = 313; (x+2)2+(x-2)2 (x-2)(x+2) = 103; x2+4x+4+ x2-4x+4x2-4 = 103;

2(x2+4)x2-4 = 103, x ≠ ± 2; 3(x² + 4) = 5(x² – 4); 3x² + 12 = 5x² – 20;

12 + 20 = 5x² – 3x²; 2x² = 32; x² = 16; x = ± 4.