Toán Lớp 6: |x+y-5|+|2x-y-1|=0 |y+5|+|x-y|=0 Nhanh meeeeeeeeeeee

Question

Toán Lớp 6:  |x+y-5|+|2x-y-1|=0 |y+5|+|x-y|=0 Nhanh meeeeeeeeeeee

thuminhthong · Answer

Giải đáp:   $  $   a,   |x+y-5| + |2x-y-1|=0   Với mọi x,y c&oacute; : |x+y-5| &ge; 0, |2x-y-1| &ge;0   -> |x+y-5| + |2x-y-1| &ge;0&forall;x,y   Dấu '=' xảy ra khi :   &harr; |x+y-5|=0, |2x-y-1|=0   &harr;x+y-5=0, 2x-y-1=0   &harr;x+y=5, 2x-y=1   &harr;x=5-y, 2x=1+y   &harr; x =5-y, 2 (5-y)=y+1   &harr; x = 5-y, -2y + 10=y+1   &harr; x=5-y, -2y-y=-10+1   &harr; x=5-y,-3y=-9   &harr;x=5-3,y=3   &harr;x=2,y=3   Vậy (x;y) = (2;3)   b,   |y+5| + |x-y|=0   Với mọi x,y c&oacute; : |y+5| &ge; 0, |x-y|&ge;0   -> |y+5| + |x-y| &ge;0&forall;x,y   Dấu '=' xảy ra khi :   &harr; |y+5|=0, |x-y|=0   &harr;y+5=0, x-y=0   &harr; y=-5, x=y =-5   Vậy (x;y) = (-5;-5)

tuanh · Answer

Giải đáp:

|y+5|+|x-y|=0

Do |y+5| >= 0 AAy

|x-y| >= 0 AAx,y

-> |y+5|+|x-y| >= 0 AAx,y

Dấu ”=” xảy ra <=> |y+5| = 0; |x-y| = 0

-> y+5 = 0; x-y = 0

-> y = -5; x+5 = 0

-> y=-5; x = -5

Vậy (x,y) = (-5,-5)

|x+y-5|+|2x-y-1|=0

Do |x+y-5| >= 0

|2x-y-1| >= 0

-> |x+y-5|+|2x-y-1| >= 0

Dấu ”=” xảy ra <=> |x+y-5| = 0 ; |2x-y-1| = 0

-> x+y-5 = 0; 2x-y-1=0

-> x+y = 5; 2x-y = 1

-> x = 5-y; 2(5-y) – y =1

-> x=5-y; 10 – 2y – y =1

-> x=5-y; 10 -3y =1

-> x=5-y; 3y = 9

-> x = 5-y; y =3

-> x = 5 – 3; y=3

-> x = 2;y=3

Vậy (x,y) = (2,3)