a+1/a=5
a^2+1=5a
a^2=5a-1

a•a^4•a^2-109a^4-114a=
a•a^2(25a^2-10a+1)-109a^4-114a=
a•a^2(125a-25-10a+1)-109a^4-114a=
a^3(115a-24)-109a^4-114a=
6a^4-24a^3-114a=
6(115a-24)-24a(5a-1)-114a=
600a-144-120a^2=
600a-144-120(5a-1)=-144+120=-24

R=ab+bc+ca
A=√r1. B=√r2. C=√r3
R=12+15+20=47😑😐

-> a^2+b^2+c^2=121-6=115

(a+b+c)(a^2+b^2+c^2)=115*11
a^3+b^3+c^3+11*3-3abc=115*11
a^3+b^3+c^3=827

x+1/x=6
x^3+1/x^3=216-3•6=198
x^6-198x^3=-1

=-1+x^3+35(6-x)+1=x(x^2-35)+35*6=
x(6x-36)+35*6=6(6x-1)-36x+35*6=
-6+210=204

Please solve and send solution

a(x+y)=b(x-y)=2ab

2ab=b(x-y)
2a=x-y
2b=x+y => 2x=2(a+b), x=a+b
=> y=x-2a=b-a

2(x^2+y^2)=2(2a^2+2b^2)=
4(a^2+b^2)

D

=>
x^2+2xy+y^2=3
x^2-2xy+y^2=2
{(+) x^2+y^2=2.5
{(-) 4xy=1

8xy(x^2+y^2)=1•5=5

C

sin10sin20sin40sin60=
cos80sin60*1/2(cos20-cos60)=
✔️3/4*cos80cos20-✔️3/8*cos..
=
✔️3/8(cos60-cos100)-✔️3/8cos80=
✔️3/8*cos60+sqrt(3)/8cos80-sqrt(3)/8cos80=

=> root(3)/8•1/2=root(3)/16

A

Please solve and send solution

x^2-2x+4=0
x1+x2=2
x1•x2=4

a^3/b^2+b^3/a^2=-p
(a^5+b^5)/a^2b^2=-p

a^5+b^5=(a+b)^5-5ab(a^3+b^3)-10a^2b^2(a+b)=32-20•(2^3-3*4*2)-10*16*2
a^5+b^5=32

-p=32/(4*4)=2

a^3/b^2•b^3/a^2=q
a•b=q -> q=4

x^2+px+q=0
x^2-2x+4=0

C

√a = x, √b = y

x³ + y³ = 32

xy(x + y) = 31

(x + y)³ - 3*31 = 32

(x + y) = 5

xy = 31/5

x² + y² = 25 - 2*31/5 = 63/5 = a + b

Put

9