Question

If a+b+c=15 find the value of (5-a)^3 + (5-b)^3 (5-c)^3 - 3(5-a)(5-b)(5-c)​

Answer 1

Step-by-step explanation:

let a =5-a,

b =5-b

c= 5-c

now,

(5-a)^3+(5-b)^3+(5-c)^3-3(5-a)(5-b)(5-c)

we can write that,

a^3+b^3+c^3-3abc

=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)

now,put the values of a,b and c,

=[(5-a)+(5-b)+(5-c)][(5-a)^2+(5-b)^2+(5-c)^2-(5-a)(5-b)-(5-b)(5-c)-(5-a)(5-c)]

=[15-(a+b+c)][(5-a)^2+(5-b)^2+(5-c)^2-(5-a)(5-b)-(5-b)(5-c)-(5-a)(5-c)]

now,put the values of a+b+c =15,

=[15-15][(5-a)^2+(5-b)^2+(5-c)^2-(5-a)(5-b)-(5-b)(5-c)-(5-a)(5-c)]

=[0][(5-a)^2+(5-b)^2+(5-c)^2-(5-a)(5-b)-(5-b)(5-c)-(5-a)(5-c)]

=0

therefore, the value of (5-a)^3+(5-b)^3+(5-c)^3-3(5-a)(5-b)(5-c) is 0