x=6-y
y*(6-y)=7
6y-y²-7=0
y²-6y+7=0
D=36-28= 8
y1= (6+2√2)/2= 3+√2
y2= (6-2√2)/2= 3-√2
x1= 6-3-√2=3-√2
x2= 6-3+√2= 3+√2
1) (3-√2; 3+√2)
(3-√2-3-√2)²= (-2√2)²= (-√8)²=8
((3-√2)²)²+((3+√2)²)²= (9-6√2+2)²+(9+6√2+2)²= (11-6√2)²+(11+6√2)²= 121-132√2+72+121+132√2+72= 386
2) (3+√2; 3-√2)
(3+√2-3+√2)²= (2√2)²=8
((3+√2)²)²+((3-√2)²)²= (9+6√2+2)²+(9-6√2+2)²= (11+6√2)²+(11-6√2)²= 121+132√2+72+121-132√2+72= 386
Объяснение:т.к. x+y=6, (x+y)²=36т.е. х²+у²+2ху=36⇒х²+у²=36-2ху и
х²+у²=36-2·7, х²+у²=22.
имеем, (х-у)²=х²+у²-2ху=22-2·7=8.
х^4+y^4=(x²+y²)²-2x²y²=22²-2·7²=484-98=386.
x=6-y
y*(6-y)=7
6y-y²-7=0
y²-6y+7=0
D=36-28= 8
y1= (6+2√2)/2= 3+√2
y2= (6-2√2)/2= 3-√2
x1= 6-3-√2=3-√2
x2= 6-3+√2= 3+√2
1) (3-√2; 3+√2)
(3-√2-3-√2)²= (-2√2)²= (-√8)²=8
((3-√2)²)²+((3+√2)²)²= (9-6√2+2)²+(9+6√2+2)²= (11-6√2)²+(11+6√2)²= 121-132√2+72+121+132√2+72= 386
2) (3+√2; 3-√2)
(3+√2-3+√2)²= (2√2)²=8
((3+√2)²)²+((3-√2)²)²= (9+6√2+2)²+(9-6√2+2)²= (11+6√2)²+(11-6√2)²= 121+132√2+72+121-132√2+72= 386
Объяснение:т.к. x+y=6, (x+y)²=36т.е. х²+у²+2ху=36⇒х²+у²=36-2ху и
х²+у²=36-2·7, х²+у²=22.
имеем, (х-у)²=х²+у²-2ху=22-2·7=8.
х^4+y^4=(x²+y²)²-2x²y²=22²-2·7²=484-98=386.