225б
2(b²+1)/b+5b/(b²+1)=7
(b²+1)/b=a
2a+5/a=7
2a²-7a+5=0
D=49-40=9
a1=(7-3)/4=1⇒(b²+1)/b=1
b²-b+1=0,b≠0
D=1-4=-3<0 нет решения
a2=(7+3)/4=5/2⇒(b²+1)/b=5/2
2b²-5b+2=0,b≠0
D=25-16=9
b1=(5-3)/4=0,5
b2=(5+3)/4=2
Ответ b=0,5;b=2
226б
12/(y²-2y+3-(y²-2y)=-1
y²-2y=a
12/(a+3)-a=-1
12-a²-3a+a+3=0,a≠-3
a²+2a-15=0
a1+a2=-2 U a1*a2=-15
a1=-5⇒y²-2y=-5
y²-2y+5=0
D=4-20=-18<0 нет решения
a2=3⇒y²-2y=3
y²-2y-3=0
y1+y2=2 U y1*y2=-3
y1=-1 U y2=3
Ответ y=-1;y=3
228б
1/(p^4+5)-1/(p^4+7)=1/24
24(p^4+7-p^4-5)=(p^4+5)(p^4+7)
p^8+5p^4+7p^4+35-48=0
p^8+12p^4-13=0
p^4=a
a²+12a-13=0
a1+a2=-12 U a1*a2=-13
a1=-13⇒p^4=-13 нет решения
a2=1⇒p^4=1⇒p=-1 U p=1
Ответ p=-1;p=1
229б
x³-1/x³=5 1/9(x-1/x)
x³-1/x³=(x-1/x)³+3(x-1/x)
(x-1/x)³+3(x-1/x)=5 1/9(x-1/x)
x-1/x=a
a³+3a-5 1/9*a=0
a³-2 1/9*a=0
a(a²-2 1/9)=0
a=0⇒x-1/x=0
x²-1=0,x≠0
x²=1
x=-1 U x=1
a²-2 1/9=0
a²=19/9
a=-√19/3⇒x-1/x=-√19/3
3x²+√19x-3=0,x≠0
D=19+36=55
x=(-√19-√55)/6 U x=(-√19+√55)/6
a=√19/3⇒x-1/x=√19/3
3x²-√19x-3=0
x=(√19-√55)/6 U x=(√19+√55)/6
Ответ x={-1;1;(-√19-√55)/6;(-√19+√55)/6;(√19-√55)/6;(√19+√55)/6}
1) (a-z)(a+z)=a²+az-za-z²=a²-z²
2) (a+p)(a-p)=a²-ap+pa-p²=a²-p²
3) (f+5)(5-f)=5f-f²+25-5f=-f²+25=25-f²
4) (10+b)(10-b)=100-10b+10b-b²=100-b²
5) (7x-8y)(7x+8y)=49x²+56xy-56yx-64y²=49x²-64y²
6) (1-k)(k+1)=k+1-k²-k=1-k²
<span>7) (3d</span>²<span>-4p)(3d</span>²<span>+4p)=9d</span>⁴+12pd²-12pd²-16p²=9d⁴-16p²
