B) x²+2x = x²+24; 2 7 г) 4 r) 3x²+x_2-7x - 3x²+17 2. При каких значениях ці = 5 10

2. При каких значениях?

B)

$$ \frac{x^2+2x}{2} = \frac{x^2+24}{7} $$

Решим уравнение:

$$ 7(x^2+2x) = 2(x^2+24) $$

$$ 7x^2+14x = 2x^2+48 $$

$$ 5x^2+14x-48 = 0 $$

$$ D = 14^2 - 4 \cdot 5 \cdot (-48) = 196 + 960 = 1156 = 34^2 $$

$$ x_1 = \frac{-14 + 34}{2 \cdot 5} = \frac{20}{10} = 2 $$

$$ x_2 = \frac{-14 - 34}{2 \cdot 5} = \frac{-48}{10} = -4.8 $$

г)

$$ \frac{3x^2+x}{4} = \frac{2-7x}{5} = \frac{3x^2+17}{10} $$

$$ \frac{3x^2+x}{4} = \frac{2-7x}{5} $$

$$ 5(3x^2+x) = 4(2-7x) $$

$$ 15x^2+5x = 8-28x $$

$$ 15x^2+33x-8 = 0 $$

$$ D = 33^2 - 4 \cdot 15 \cdot (-8) = 1089 + 480 = 1569 = 39.61^2 $$

$$ x_1 = \frac{-33 + 39.61}{2 \cdot 15} = \frac{6.61}{30} = 0.22 $$

$$ x_2 = \frac{-33 - 39.61}{2 \cdot 15} = \frac{-72.61}{30} = -2.42 $$

$$ \frac{2-7x}{5} = \frac{3x^2+17}{10} $$

$$ 10(2-7x) = 5(3x^2+17) $$

$$ 20-70x = 15x^2+85 $$

$$ 15x^2+70x+65 = 0 $$

$$ 3x^2+14x+13 = 0 $$

$$ D = 14^2 - 4 \cdot 3 \cdot 13 = 196 - 156 = 40 = 6.32^2 $$

$$ x_1 = \frac{-14 + 6.32}{2 \cdot 3} = \frac{-7.68}{6} = -1.28 $$

$$ x_2 = \frac{-14 - 6.32}{2 \cdot 3} = \frac{-20.32}{6} = -3.39 $$

Ответ: B) x = 2; x = -4.8; г) x = 0.22; x = -2.42; x = -1.28; x = -3.39