Question

30/(15+x)+30/(15-x)=4,5
x=?

Answer 1

$\frac{30}{15 + x} + \frac{30}{15 - x} = 4.5 \\ \\ \frac{30}{15 + x} + \frac{30}{15 - x} - 4.5 = 0 \\ \\ \frac{30}{15 + x} + \frac{30}{15 - x} - \frac{9}{2} = 0 \\ \\ \frac{60 \times (15 - x) + 60 \times(15 + x) - 9 \times (15 - x)(15 + x) }{2(15 - x)(15 + x)} = 0 \\ \\ \frac{900 - 60x + 900 + 60x - 9 \times ( {15}^{2} - {x}^{2} )}{2(15 - x)(15 + x)} = 0\\ \\ \frac{1800 - 9 \times {15}^{2} - 9 {x}^{2} }{2(15 - x)(15 + x)} = 0 \\ \\ \frac{1800 - 9 \times 225- 9 {x}^{2} }{2(15 - x)(15 + x)} = 0 \\ \\ \frac{1800 - 2025 - 9 {x}^{2} }{2(15 - x)(15 + x)} = 0 \\ \\ \frac{ - 225 - 9 {x}^{2} }{2(15 - x)(15 + x)} = 0$
Если частное чисел равно 0, то и числитель равен 0.

$- 225 + 9 {x}^{2} = 0 \\ \\ 9 {x}^{2} = 225 \\ \\ {x}^{2} = 225 \div 9 \\ \\ {x}^{2} = 25 \\ \\ x _{1} = - 5 \\ x_{2} = 5$
Ответ: х1 = -5
х2 = 5