Question

Rozwiaz rownamie za pomoca wzorow skroconego mnozenia: a) (6+1/2x)(-1/3x+6)+(1/3x-4)do potegi drugiej=4 b) (-4x-3)(4x-3)+8(1-pierwiastek z dwoch. x)kwadrat=1

Answer 1

 

Answer 2

a)

(6+1/2x)(-1/3x+6)+(1/3x-4)² = 4

-2x + 36 - 1/6x² + 3x + 1/9x² - 8/3x + 16 = 4

52 - 1/6x² + 1/9x² - 5/3x  = 4

 - 1/6x² + 1/9x² - 5/3x  = 4- 52

 - 1/6x² + 1/9x² - 5/3x  = -48  /*18

-3x² + 2x² - 30x = -864

-x² - 30x + 864 = 0

x² + 30x - 864 = 0

Δ = 30² - 4 * 1 * (-8864) = 900 + 3456 = 4356

√Δ = 66

x1 = (-30 - 66)/2 = -96/2 = -48

x2 = (-30 + 66)/2 = 36/3 = 18

 

 

b)

(-4x-3)(4x-3)+8(1-√2 x)² = 1

-(4x + 3)(4x - 3) + 8(1 - √2 x)² = 1

-(16x² - 9) + 8(1 - 2√2x + 2x²) = 1

-16x² + 9 + 8 - 16√2x + 16x² = 1

-16√2x = 1 - 17

-16√2x = -16

√2x = 1    /:√2

x = 1/√2

x = √2/2