1
Question
Q1. Find the value of (x-a)3+(x-b)3+(x-c)3-3(x-a)(x-b)(x-c), if a+b+c=3x.
Q1. Find the value of (x-a)3+(x-b)3+(x-c)3-3(x-a)(x-b)(x-c), if a+b+c=3x.
Open in App
Solution
We know that,
a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)
If a+b+c=0 then,
a³+b³+c³-3abc=0×(a²+b²+c²-ab-bc-ca)=0 .....(1)
(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)
let a=(x-a)
b=(x-b)
and c=(x-c)
a+b+c=x-a+x-b+x-c=3x-(a+b+c)=3x-3x=0....(as a+b+c=3x)
(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)=0
Thus the answer is 0....
Read more on Brainly.in - https://brainly.in/question/1250191#readmore
a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)
If a+b+c=0 then,
a³+b³+c³-3abc=0×(a²+b²+c²-ab-bc-ca)=0 .....(1)
(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)
let a=(x-a)
b=(x-b)
and c=(x-c)
a+b+c=x-a+x-b+x-c=3x-(a+b+c)=3x-3x=0....(as a+b+c=3x)
(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)=0
Thus the answer is 0....
Read more on Brainly.in - https://brainly.in/question/1250191#readmore
Suggest Corrections
3
Similar questions