Вправи: 1384

1384. Розв’яжи рівняння.

a) x-1x+5 + x-1x-5 = 2; x-1x-5+(x-1)(x+5)(x+5)(x-5) = 2;

(x-1)(x-5+ x+5)(x+ 5)(x-5) = 2; x-1•2x(x+5)(x-5) = 2; x ≠ 5, x ≠ –5;

2x(x – 1) = 2(x² – 25); x(x – 1) = x² – 25; x² – x – x² = –25; x = 25;

б) 2x-1x+2 = 1-2xx-2 + 4; 2x-1x+2 + 2x-1x-2 = 4; (2x – 1)( 1x+2 + 1x-2) = 4;

(2x – 1)( x-2+ x+2x2- 4) = 4; (2x – 1) • 2x = 4(x² – 4);

x ≠ 2, x ≠ –2; 4x² – 2x = 4x² – 16; 2x = 16; x = 8;

в) x-1x+4 – 2 = 1- xx-4; x-1x+4 + x-1x- 4 = 2; (x – 1)( x-4+ x+4(x-4)(x+4)) = 2;

x ≠ 4, x ≠ –4; 2x(x – 1) = 2(x² – 16); 2x² – 2x = 2x² – 32; 2x = 32;

x = 16;

г) 2x-12x+4 = 1-2x2x-4 + 2; 2x-12x+4 + 2x-12x+4 = 2; (2x – 1)( 2x-4+2x+44x2- 16) = 2;

x ≠ 2, x ≠ –2, то 4x(2x – 1) = 2(4x² – 16); 8x² – 4x = 8x² – 32;

–4x = –32; x = 8.

Відповідь: а) 25; б) 8; в) 16; г) 8.