Explanation:
1/a + 1/b + 1/c = 1/(a+b+c)
=> 1/a + 1/b = 1/(a+b+c) -1/c
=> (b+a)/ab = {c - (a+b+c)/c(a+b+c)
=> (a+b)/ab = -(a+b)/(ac+bc+c^2)
=> 1/ab = -1/(ac+bc+c^2)
=> -ab = ac+bc+c^2
=-c^2 = ab+bc+ca
Similarly we can show that
-b^2 =ab+bc+ca and -c^2 = ab+bc+ca
So a=b=c. since -a^2 = -b^2 = - c^2
Then 1/a + 1/b + 1/c = 1/(a+b+c) => 3/a= 1/3a
=> 1/a^5 + 1/b^5 + 1/c^5 =3/a^5=(( 3/a )(1/a^4)
= 1/3a × 1/a^4 = 1/3a^5 = 1/(a^5 +b^5+c^^5)
Hope it help