Question

Решите уравнения, применяя свойства пропорции. 1) x/x+1 = x-6/x-1
2) 3/x^2+2 = 1/x
3) 3/3n-1 = 2/2n-1
!

Answer 1

1.

$\frac{x}{x - 1} = \frac{x - 6}{x - 1} \\ \frac{x}{x - 1} - \frac{x - 6}{x - 1} = 0 \\ \frac{x - x - 6}{x - 1} = 0$

х≠1

$x - x - 6 = 0 \\ - 6 = 0$

утверждение ложно

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2.

$\frac{3}{x {}^{2} + 2 } = \frac{1}{x} \\ \frac{3}{ {x}^{2} + 2 } - \frac{1}{x} = 0 \\ \frac{3x - x {}^{2} - 2 }{x(x {}^{2} + 2) } = 0$

х≠2

$3x - x {}^{2} + 2 = 0 \\ - x {}^{2} + 3x - 2 = 0 /:-1 \\ x {}^{2} - 3x + 2 = 0 \\ a = 1 \: b = - 3 \: c = 2 \\ D = b {}^{2} - 4ac = ( - 3) {}^{2} - 4 \times 1 \times 2 = 9 - 8 = 1 \\ x½ = \frac{ - b± \sqrt{D} }{2a} = \frac{3±1}{2} = 2;1$

3.

$\frac{3}{3n - 1} = \frac{2}{2n - 1} \\ \frac{3}{3n - 1} - \frac{2}{2n - 1} = 0 \\ \frac{3(2n - 1) - 2(3n - 1)}{(3n - 1)(2n - 1)} = 0 \\ \frac{6n - 3 - 6n + 2}{(3n - 1)(2n - 1)} = 0 \\ \frac{ - 3 + 2}{(3n - 1)(2n - 1)}$

n≠1, n≠3, n≠2

$- 3 + 2 = 0$

утверждение ложно

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