17) (x+5)² + (x-10)² = 2x²
x² + 2*x*5 + 5² + x² - 2*x*10 + 10² = 2x²
x² + 10x + 25 + x² - 20x + 100 - 2x² = 0
-10x + 125 = 0
-10x = -125
x = 12,5
19) (x-9)² = (x-3)²
x² - 2*x*9 + 9² = x² - 2*x*3 + 3²
x² - 18x + 81 = x² - 6x + 9
x² - x² - 18x + 6x + 81 - 9 = 0
-12x - 72 = 0
- 12x = 72
x = -6
21) x² - 4x + 35 = -9x²+ 11x + 45
x² + 9x² - 4x - 11x + 35 - 45 = 0
10x² - 15x - 10 = 0
a = 10, b = -15, c = -10
D = b² - 4ac = (-15)² - 4*10*(-10) = 225 + 400 = 625
D > 0 ⇒ уравнение имеет 2 корня
x1 = (-b+√D)/2a = (-(-15)+√625)/2*10 = (15+25)/20 = 40/20 = 2
x2 = (15 - 25)/20 = -0,5