3sin^2х-4sinxcosx+5cos^2x-2=0
3sin^2х-4sinxcosx+5cos^2x-2•(sin^2x+cos^2x)=0
3sin^2х-4sinxcosx+5cos^2x-2sin^2x-2cos^2x=0
Sin^2x-4sinxcosx+3cos^x=0. (:cos^2x)
tg^2x-4tgx+3=0
tgx=t
t^2-4t+3=0
D=16-12=4
t1=(4+2):2=3
t2=(4-2):2=1
tgx=1
X=arctg1+Пк;к€Z
X=П/4+Пк;к€Z
tgx=3
X=arctg3+Пк;к€Z
(a²-b²)(a²+b²)=(a²)²-(b²)²=a⁴-b⁴
2^x*(1+2^3)=9; 2^x*9=9; 2^x=1; 2^x=2^0; x=0. Ответ: x=0.
51х-38у=130
17х-8у=90 *(-3)
51х-38у=130
-51х+24у= -270
-14у= -140
51х-38у=130
у=10
х=10