1
a)(√7-√5)-1/(√5+√7)=(7-5-1)/(√5+√7)=1/(√5+√7)
b)
2
а)9x-4x²=0
x(9-4x)=0
x=0 U x=2,25
б)49-16x²=0
(7-4x)97+4x)=0
7-4x=0⇒x=1,75
7+4x=0⇒x=-1,75
в)x²+18x-40=0
x1+x2=-18 U x1*x2=-40⇒x1=-20U x2=2
г)7x²-3x-4=0
D=9+112=121
x1=(3-11)/14=-4/7
x2=(3+11)/14=1
д)x²-(2a-5)x-10a=0
D=(2a-5)²-4*(-10a)=4a²-20a+25+40a=4a²+20a+25=(2a+5)²≥0
√D=|2a+5|
x1=(2a-5-2a-5)/2=-5
x2=(2a-5+2a+5)/2=2a
3
a
a)x²-5x-3=0
D=25+12=37>0
x1+x2=5 U x1*x2=-3
x1²+x2²=(x1+x2)²-2x1x2=5²-2*(-3)=25+6=31
b)x1/x2+x2/x1=(x1²+x2²)/x1x2=31/(-3)=-10 1/3
b
(x1+2)+(x2+2)=x1+x2+4=5+4=9
(x1+2)(x2+2)=x1x2+2(x1+x2)+4=-3+2*5+4=11
x²-9x+11=0
4
(a+2)x²-2ax+1=0
a+2≠0⇒a≠-2
D=4a²-4(a+2)=4a²-4a-8=0
a²-a-2=0
a1+a2=1 U a1*a2=-2
a1=-1 U a2=2 уравнение имеет 1 корень
5
1)√x-1/√x=(x-1)/√x
2)(√x+1)/(√x-1)-(√x-1)/(√x+1) +4√x=(x+2√x+1-x+2√x-1)/(x-1) +4√x=
=4√x/(x-1)+4√x=4√x(1+x-1)/(x-1)=4x√x/(x-1)
3)(x-1)/√x *4x√x/(x-1)=4x
Удачи!