Question

1) (12+х)^2 больше или равно х^2+21х 2) х^2 меньше (25-х)^2+25х

Answer 1

${(12 + x)}^{2} \geqslant {x}^{2} + 21x \\ 144 + 24 {x}^{2} + {x}^{2} - {x}^{2} - 21x \geqslant 0 \\ 24 {x}^{2} - 21x + 144 \geqslant 0$
нет корней

${x}^{2} < {(25 - x)}^{2} + 25x \\ {x}^{2} < 625 - 50 {x}^{2} + {x}^{2} + 25x \\ 50 {x}^{2} - 25x - 625 < 0 \\ 10x ^{2} - 5x - 125 < 0 \\ 2 {x}^{2} - x - 25 < 0 \\ x = \frac{1 + - \sqrt{201} }{4} \\ x = \frac{5 \times (1 + - \sqrt{201)} }{4} = 1.25(1 + - \sqrt{201} )$