Simplify:
(a²-b²)³ + (b²-c²)³ + (c²-a²)³/
(a-b)³ + (b-c)³ + (c-a)³
Answers
Answered by
1
Answer:
let a
2
−b
2
=x
1
;b
2
−c
2
=y
1
;c
2
−a
2
=z
1
x
1
+y
1
+z
1
=0
⇒x
1
3
+y
1
3
+z
1
3
=3x
1
y
1
z
1
=3(a
2
−b
2
)(b
2
−c
2
)(c
2
−a
2
)
let a−b=x
2
;b−c=y
2
;c−a=z
2
x
2
+y
2
+z
2
=0
⇒x
2
3
+y
2
3
+z
2
3
=3x
2
y
2
z
2
=3(a−b)(b−c)(c−a)
So,
x
2
3
+y
2
3
+z
2
3
x
1
3
+y
1
3
+z
1
3
=(a+b)(b+c)(c+a)
Answered by
2
Answer:
we use the fact that if a+b+c=0 then a^3+b^3+c^3=abc.
(a^2-b^2)+(b^2-c^2)+(c^2+a^2)=0
also (a-b) + (b-c) + (c-a) =0
we assume that a≠b≠c.
hence
(a^2-b^2)^3 + (b^2-c^2)^3 + (c^2-a^2)^3 ÷ (a-b)^3 + bc)^3+ (c-a)^3
=3(a^2-b^2) (b^2-c^2) (c^2-a^2) / [3 (a-b) (b-c) (c-a)]
= (a+b) (b+c) (c+a)
therefore, a^2-b^2 = (a-b) (a+b) and similarly other terms.
Step-by-step explanation:
Mark me as brainlists
Similar questions