<span>2а(3а-5)-(а-3)(а-7)=2а*3а-2а*5-а^2-21=6a^2-10a-16a=a^2</span>
1) 7а - ( а + 4 ) - ( 5а - 1 ) - 8 = 7а - а - 4 - 5а + 1 - 8 = ( 7а - а - 5а ) + ( - 4 + 1 - 8 ) = а - 11
Ответ ( а - 11 )
2) 5b - ( 2b - ( b - 2 ) + ( 3 - 2b ) - 13 ) = 5b - ( 2b - b + 2 + 3 - 2b - 13 ) = 5b - ( - b - 8 ) = 5b + b + 8 = 6b + 8
Ответ ( 6b + 8 )
6.
sin51°cos39°-sin21°cos9°=sin(90°-39°)cos39°-sin21°cos9<span>°=
=cos39</span>°cos39°-sin(30°-9°)cos9°=cos²39°-sin(30°-9°)cos9<span>°=
=(cos(30</span>°+9°))² - (sin30°cos9°-cos30°sin9°)cos9<span>°=
=(cos30</span>°cos9°-sin30°sin9°)² - (¹/₂ cos9° - (√3/2) sin9°)cos9<span>°=
=((</span>√3/2) cos9° - ¹/₂ sin9°)² - ¹/₂ cos² 9° + (√3/2) sin9° cos9<span>° =
= </span>³/₄ cos² 9° - (√3/2)sin9° cos9° + ¹/₄ sin² 9° - ¹/₂ cos² 9° + +(√3/2)sin9°cos9<span>°=
= </span>³/₄ cos² 9° - ²/₄ cos² 9° + ¹/₄ sin² 9<span>° =
= </span>¹/₄ cos² 9° + ¹/₄ sin² 9<span>° =
= </span>¹/₄ (cos² 9° + sin² 9<span>°</span>)= ¹/₄ * 1 = ¹/₄
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!