Предмет: Алгебра, автор: feliciaveberr

решите уравнение 10^2=(2+х)^2+(2+10-x)^2

Ответы

Автор ответа: CodedEmerald

Ответ:

x₁ = 6

x₂ = 4

Объяснение:

10² = (2 + х)² + (2 + 10 - x)²

100 = (2 + x)² + (12 - x)²

100 = 4 + 4x + x² + 144 - 24x + x²

100 = 148 - 20x + 2x²

2x² - 20x + 48 = 0

D = b² - 4ac = (-20)² - 4 * 2 * 48 = 400 - 384 = 16

x₁,₂ = (-b ± √D)/2a = (-(-20) ± √16)/2*2 = (20 ± 4)/4

x₁ = 24/4 = 6

x₂ = 16/4 = 4

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