Question

Уравнение решить помогите

Answer 1

$(x - 3)(x - 4)(x - 5) = (x - 2)(x - 4)(x - 5) \\ (x - 3)(x - 4)(x - 5) - (x - 2)(x - 4)(x - 5) = 0 \\ (x - 4)(x - 5)(x - 3 - (x - 2)) = 0 \\ (x - 4)(x - 5)(x - 3 - x + 2) = 0 \\ (x - 4)(x - 5) \times ( - 1) = 0 \\ (x - 4)(x -5) = 0 \\ x = 4 \\ x = 5$
Ответ: 4; 5.

$\frac{4}{x - 9} + \frac{9}{x - 4} = 2 \\ \frac{4(x - 4) + 9(x - 9) }{(x - 9)(x - 4)} = \frac{2(x - 9)(x - 4)}{(x - 9)(x - 4)} \\ \frac{4x - 16 + 9x - 81 - 2(x - 9)(x - 4)}{(x - 9)(x - 4)} = 0 \\ \frac{13x - 97 - 2( {x}^{2} - 9x - 4x + 36) }{(x - 9)(x - 4)} = 0 \\ \frac{13x - 97 - 2 {x}^{2} + 18x + 8x - 72}{(x - 9)(x - 4)} = 0 \\ \frac{ - 2 {x}^{2} + 39x - 169}{(x - 9)(x - 4)} = 0 \\ 2 {x}^{2} - 39x + 169 = 0 \\ d = {b}^{2} - 4ac = 1521 - 4 \times 2 \times 39 = 169 \\ x1 = \frac{39 + 13}{2 \times 2} = \frac{52}{4} = 13 \\ x2 = \frac{39 - 13}{2 \times 2} = \frac{26}{4} = \frac{13}{2}$
Ответ: 13/2; 13.