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tea74
@tea74
November 2021
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Задания номер: 331(бгез), 334, 336(бг), 338(бг). Заранее спасибо!
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sedinalana
Verified answer
331
б)c(c-2)x=c²-4
x=(c-2)(c+2)/c(c-2)=(c+2)/c,c≠0 U c≠2
г)ax+5a=30+6x
ax-6x=30-5a
x=5(6-a)/(a-6)=-5,a≠6
е)b²x-x=b²+4b-5
x(b²-1)=(b+5)(b-1)
x=(b+5)(b-1)/(b-1)(b+1)=(b+5)/(b-1\+1),b≠1 U b≠-1
з)(a²+1)x+a(a-2x)=1
(a²+1)x-2ax=1-a²
x(a²-2a+1)=1-a²
x=(1-a)(1+a)/(1-a)²=(1+a)/(1-a),a≠1
336
б)ax²+8x+4=0
D=64-16a>0
16a<64
a<4
a∈(-∞;4)
г)3x²+(2a+3)x+(a+2)=0
D=(2a+3)²-12(a+2)=4a²+12a+9-12a-24=4a²-15>0
(2a-√15)(2a+√15)>0
a=√15/2 a=-√15/2
a∈(-∞;-√15/2) U (√15/2;∞)
338
б)bx²-16x+8=0
D=256-32b<0
32b>256
b>8
b∈(8;∞)
г)(b-3)x²-2(b-3)(b+3)=0
D=4(b-9)²-4(b-3)(b+3)=4b²-72b+324-4b²+36<0
-72b+360<0
72b>360
b>5
b∈(5;∞)
334
9x²+6xp+12x+p²+4p+4-9x²+6xp-6x-p²+2p-1-12x-4=0
12xp-6x+6p-1=0
6x(2p-1)=1-6p
x=(1-6p)/(2p-1)
1)(1-6p)/(2p-1)<0
p=1/6 p=1/2
p∈(-∞;1/6) U (1/2;∞)
2)-1/2<(1-6p)/(2p-1)<1/2
{(1-6p)/(2p-1)>-1/2⇒(2-12p+2p-1)/2(2p-1)>0⇒(1-10p)/(2p-1)>0⇒1/10<p<1/2
{(1-6p)/(2p-1)<1/2⇒(2-12p-2p+1)/2(2p-1)<0⇒(3-14p)/(2p-1)<0⇒p<3/14 U p>1/2
p∈(1/10;3/14)
2 votes
Thanks 2
tea74
Спасибо!
tea74
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Answers & Comments
Verified answer
331б)c(c-2)x=c²-4
x=(c-2)(c+2)/c(c-2)=(c+2)/c,c≠0 U c≠2
г)ax+5a=30+6x
ax-6x=30-5a
x=5(6-a)/(a-6)=-5,a≠6
е)b²x-x=b²+4b-5
x(b²-1)=(b+5)(b-1)
x=(b+5)(b-1)/(b-1)(b+1)=(b+5)/(b-1\+1),b≠1 U b≠-1
з)(a²+1)x+a(a-2x)=1
(a²+1)x-2ax=1-a²
x(a²-2a+1)=1-a²
x=(1-a)(1+a)/(1-a)²=(1+a)/(1-a),a≠1
336
б)ax²+8x+4=0
D=64-16a>0
16a<64
a<4
a∈(-∞;4)
г)3x²+(2a+3)x+(a+2)=0
D=(2a+3)²-12(a+2)=4a²+12a+9-12a-24=4a²-15>0
(2a-√15)(2a+√15)>0
a=√15/2 a=-√15/2
a∈(-∞;-√15/2) U (√15/2;∞)
338
б)bx²-16x+8=0
D=256-32b<0
32b>256
b>8
b∈(8;∞)
г)(b-3)x²-2(b-3)(b+3)=0
D=4(b-9)²-4(b-3)(b+3)=4b²-72b+324-4b²+36<0
-72b+360<0
72b>360
b>5
b∈(5;∞)
334
9x²+6xp+12x+p²+4p+4-9x²+6xp-6x-p²+2p-1-12x-4=0
12xp-6x+6p-1=0
6x(2p-1)=1-6p
x=(1-6p)/(2p-1)
1)(1-6p)/(2p-1)<0
p=1/6 p=1/2
p∈(-∞;1/6) U (1/2;∞)
2)-1/2<(1-6p)/(2p-1)<1/2
{(1-6p)/(2p-1)>-1/2⇒(2-12p+2p-1)/2(2p-1)>0⇒(1-10p)/(2p-1)>0⇒1/10<p<1/2
{(1-6p)/(2p-1)<1/2⇒(2-12p-2p+1)/2(2p-1)<0⇒(3-14p)/(2p-1)<0⇒p<3/14 U p>1/2
p∈(1/10;3/14)