Question

b)x-2x+3x-4x+…+99x-100x=-30
C)17x+18x+…+45x=899

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Answer 1

Răspuns:

b) 3/5; c) 1

Explicație pas cu pas:

$x(1 - 2 + 3 - 4 + ... + 99 - 100) = - 30 \\ x((1 + 2 + 3 + ... + 99 + 100) - 2 \times (2 + 4 + 6 + ... + 100)) = - 30 \\ x((1 + 2 + 3 + ... + 99 + 100) - 2 \times 2 \times (1 + 2 + 3 + ... + 50)) = - 30 \\ x( \frac{100 \times 101}{2} - \frac{2 \times 2 \times 50 \times 51}{2} ) = - 30 \\ x( \frac{100 \times 101}{2} - \frac{100 \times 102}{2} ) = - 30 \\ \frac{x \times 100 \times ( - 1)}{2} = - 30 \\ x = \frac{ 2 \times (- 30)}{ - 100} \\ x = \frac{3}{5}$

$x(17 + 18 + .. + 45) = 899 \\ x((1 + 2 + 3 + ... + 45) - (1 + 2 + 3 + ... + 16)) = 899 \\ x( \frac{45 \times 46}{2} - \frac{16 \times 17}{2} ) = 899 \\ x \times \frac{2070 - 272}{2} = 899 \\ x = \frac{899 \times 2}{1798} = \frac{1798}{1798} \\ x = 1$