Grade 99 grade maths
if a+b+c=0 prove a^4+b^4+c^4 = 2(a^2b^2+b^2c^2+c^2a^2)
if a+b+c=0 prove a^4+b^4+c^4 = 2(a^2b^2+b^2c^2+c^2a^2)
1 Answer
Gursimran Singh
if a+b+c=0 the (a+b+c)^2 = 0
a^2+b^2+c^2+2(ab+bc+ca) = 0
a^2+b^2+c^2 = -2(ab+bc+ca) squaring on both sides
a^4+b^4+c^4+2(a^2b^2+b^2c^2+c^2a^2) = 4(a^2b^2+b^2c^2+c^2a^2+2(ab^2c+bc^2a+ca^2b))
a^4+b^4+c^4 = 4(a^2b^2+b^2c^2+c^2a^2+2(ab^2c+bc^2a+ca^2b))-2(a^2b^2+b^2c^2+c^2a^2)
= 2[2(a^2b^2+b^2c^2+c^2a^2+(ab^2c+bc^2a+ca^2b))-(a^2b^2+b^2c^2+c^2a^2)]
= 2((a^2b^2+b^2c^2+c^2a^2+(ab^2c+bc^2a+ca^2b)))
Other Related Questions on 9 grade maths
What are the differences between similar triangles and congruent triangles?
What are the differences between similar triangles and congruent triangles?
9 grade maths
Last Activity: 11 Months ago
The L.C.M of the smallest 2 digit composite number and the smallest composite number is:
- (a) 12
- (b) 4
- (c) 20
- (d) 44
The L.C.M of the smallest 2 digit composite number and the smallest composite number is:
- (a) 12
- (b) 4
- (c) 20
- (d) 44
9 grade maths
Last Activity: 0 Years ago