675.

a)

[tex](2x - 1)( {x}^{2} + x - 3) < (x + 3)(2 {x}^{2} - 5x + 8) \\ 2 {x}^{3} + 2 {x}^{2} - 6x - {x}^{2} - x + 3 < 2 {x}^{3} - 5 {x}^{2} + 8x + 6 {x}^{2} - 15x + 24 \\ 2 {x}^{3} + {x}^{2} - 7x + 3 < 2 {x}^{3} + {x}^{2} - 7x + 24 \\ 2 {x}^{3} + {x}^{2} - 7x + 3 - 2 {x}^{3} - {x}^{2} + 7x < 24 \\ 3 < 24[/tex]

Неравенство истинно при любом значении х

б)

[tex]( {y}^{2} - 1)( {y}^{4} + {y}^{2} + 1) > ( {y}^{3} - 2)( {y}^{3} + 2) \\ {y}^{6} + {y}^{4} + {y}^{2} - {y}^{4} - {y}^{2} - 1 > ( {y}^{3} ) {}^{2} - 2 {}^{2} \\ {y}^{6} - 1 > {y}^{6 } - 4 \\ {y}^{6} - 1 - {y}^{6} > - 4 \\ - 1 > - 4 \: \: | \times ( - 1) \\ 1 < 4[/tex]

Неравенство истинно при любом значении х