Математика

[Chacho]

Някой за помощ:
1. √12 - √3 - ...

1.√12-√3-√0,03-√0,75 = √3.4-√3-√3.√1/100 - √75/100 = √3.√4-√3-√3.√(1/10)(1/10) - √3/4 = √3(√4-√(1/10.10)-√1/4) = √3(2-1/10-1/2)=√3(14/10)=7√3 / 5

2.(8+3√5)(2-√5)=16-2√5-3.(√5)²=16-2√5-3.5 = 1-2√5

3.√60+(√3-√5)²=√4.15+√3²-2.√3.√5+√5²=2.√15+3-2.√15+5=3+5=8

4.x²-13=0
x²=13
x=±√13

5.
x²-2√2.x+2=0
x²-2√2.x+√2²=0
(x-√2)²=0
x=√2

6.
x²-(1+√3)x+√3=0
D=(1+√3)²-√3=1+2.√3+√3²-4.√3=1-2√3+3=(1-√3)²
x1=(1+√3-(1-√3)) /2 =2√3/2=√3
x2=(1+√3+1-√3)/2 = 2/2 = 1

7.
(ax-1)² - (x-a)² = 1
(ax-1+x-a)(ax-1-x+a)=1
(x(a+1)-(a+1))(x(a-1)+(a-1))=1
(x-1)(a+1)(x+1)(a-1)=1
(x²-1)(a²-1)=1
При а=1
(x²-1).0=1
Няма решение
При а=/=1
x²-1=1/(a²-1)
x²=(1+(a²-1))/(a²-1)

ДМ:
(1+(a²-1))/(a²-1) >=0
a²-1=-1
a²=0
a=0

a²-1=0
a=±1

_-_-1_+_0_-_1__+__

При a E (-1;0] U (1;+безкр)

x=±√[(1+(a²-1))/(a²-1)]

Мисля, че са така