3 / (√3+√2) + 5 / (√3-√2) =
= 3*(√3-√2) / ( (√3+√2)(√3-√2) ) + 5*(√3+√2) / ( (√3+√2)(√3-√2) ) =
= ( 3*(√3-√2) + 5*(√3+√2)) / ( (√3+√2)(√3-√2) ) =
= ( 3√3 -3√2 + 5√3+5√2 ) / ( (√3) ^2-(√2)^2 ) =
= (8√3 + 2√2) / (3 - 2) = 8√3 + 2√2
(x-3)(x+5) - (2x+3)(x-4) = 0
x² +5x -3x -15 - (2x² -8x + 3x - 12) =0
x² +2x -15 - (2x² - 5x - 12) =0
x² + 2x - 15 - 2x² + 5x + 12 = 0
(x² -2x²) + (2x + 5x) + (-15 + 12) = 0
- x² + 7x - 3 = 0 |*(-1)
x² - 7x + 3 = 0
D = (-7)² - 4*1*3 = 49 - 12 = 37
x₁ = ( - (-7) -√37)/ (2*1) = (7-√37)/2 = 0.5(7-√37) = 3.5 - 0.5√37
x₂ = (7 +√37)/2 = 3.5 + 0.5√37
2х в кв + х - 21х= -8х в кв
2х в кв + х - 21х +8х в кв=0
10х в кв - 20х =0
10х(х-2)=0
10х=0 или х-2=0
х=0 х=2