Решите уравнения: 1) (5-y)^2+17=(y-3)^2 2)7x+x(x-7)=(2x+5)(5-2x)

Question

Решите уравнения: 1) (5-y)^2+17=(y-3)^2
2)7x+x(x-7)=(2x+5)(5-2x)

Answer 1

1) ( 5 - y)² + 17 = ( y - 3)²
( 5 - y)( 5 - y) + 17 = ( y - 3)( y - 3)
25 - 5y - 5y + y² + 17 = y² - 3y - 3y + 9
y² - 10y + 42 = y² - 6y + 9
y² - 10y - y² + 6y = 9 - 42
- 4y = - 33
4y = 33
y = 33/4
y = 8,25

2) 7x + x ( x - 7) = ( 2x + 5)( 5 - 2x)
7x + x² - 7x = 10x - 4x² + 25 - 10x
x² = - 4x² + 25
x² + 4x² - 25 = 0
5x² - 25 = 0
D = b² - 4ac
D = 0² - 4 × 5 × ( - 25) = 0 + 500 = 500
x₁ = 0 + √500 / 10 = 10√5 / 10 = √5
x₂ = 0 - √ 500 / 10 = - 10√5 / 10 = - √5