решите уравнение:
(x+1)/x - √((x+1)/x) - 2 = 0
(x+1)/x - √((x+1)/x) - 2 + 1/4 - 1/4 = 0
(x+1)/x - √((x+1)/x) + 1/4 = 2 + 1/4
(√((x+1)/x)- 1/2)² = 9/4
√((x+1)/x)- 1/2 = ± √(9/4)
√((x+1)/x) = 1/2 ± 3/2
√((x+1)/x) ≠ -1
√((x+1)/x) = 2
(x+1)/x = 4
x+1 = 4x
1 = 3x
x = 1/3
решите неравенство:
(x-1)(x-2)/(x-3)>0
_ 1 + 2 _ 3 +
------o----------------o----------------o--------->
x∈]1;2[∪]3;∞[
решите систему:
(1) {x/y+y/x=13/6
(2) {x+y=5 => y = 5-x подставим в (1)
x/(5-x)+(5-x)/x=13/6
(x²+(5-x)²)/(5-x)x=13/6
(x²+25-10x+x²)/(5x-x²)=13/6
(2x²-10x+25)/(5x-x²)=13/6
6(2x²-10x+25)=13(5x-x²)
12x²-60x+150=65x-13x²
25x²-125x+150=0
x²-5x+6=0 найдём корни квадратного уравнения
D = 25-24 =1
x1 = (5-1)/2 = 2 => y1 = 5-2 = 3
x1 = (5+1)/2 = 3 => y2 = 5-3 = 2