CHỨNG MINH RẰNGA. (A2+ B2) (X2+ Y2) = (AY - BX)2+ (Ã + BY)2B. (A + B...
Bài 4: Chứng minh rằng
a. (a
2
+ b
2
) (x
2
+ y
2
) = (ay - bx)
2
+ (ã + by)
2
b. (a + b + c)
2
+ a
2
+ b
2
+ c
2
= (a + b)
2
+ (b + c)
2
+ (c + a)
2
c. (x + y)
4
+ x
4
+ y
4
= 2(x
2
+ xy + y
2
)
2
Giải:
VP = (ay - bx)
2
+ (ã + by)
2
= ay
2
- 2abxy + b
2
x
2
+ a
2
x
2
+ 2abxy + b
2
y
2
= a
2
y
2
+ a
2
x
2
+ b
2
x
2
+ b
2
y
2
= a
2
(x
2
+ y
2
) + b
2
(x
2
+ y
2
)
= (a
2
+ b
2
) (x
2
+ y
2
) = VT
đpcm
VP = (a + b)
2
+ (b + c)
2
+ (c + a)
2
= a
2
+ 2ab + b
2
+ b
2
+ 2bc + c
2
+ c
2
+ 2ac + a
2
= a
2
+ b
2
+ c
2
+ 2ab + 2ac + 2bc + a
2
+ b
2
+ c
2
= (a + b + c)
2
+ a
2
+ b
2
+ c
2
= VT
đpcm
VT = (x + y)
4
+ x
4
+ y
4
= x
2
+ 4x
3
y + 6x
2
y
2
+ 4xy
3
+ y
4
+ x
4
+ y
4
= 2(x
4
+ y
4
+ x
2
y
2
+ 2x
3
y + 2xy
3
+ 2x
2
y
2
)
= 2(x
2
+ y
2
+ xy)
2