\left. \begin{array} { l } { \text { if } a + b + c = 5 \text { and }

1.	\left. \begin{array} { l } { \text { if } a + b + c = 5 \text { and } a b + b c + c a = 15 \text { find the valu } } \\ { ( a + b ) ^ { 3 } + ( b + c ) ^ { 3 } + ( c + a ) ^ { 3 } - 3 ( a + b ) ( b + c ) ( c + a ) } \end{array} \right.
Answer» (a + b)^3+ (b +c)^3+ (c + a)^3- 3(a + b)(b +c)(c + a) = 2a^3+ 2b^3+2c^3- 6abc 2a^3+ 2b^3+ 2c^3- 6abc = 2(a^3+ b^3+c^3- 3abc) = 2(a + b+ c)(a^2+ b^2+c^2- (ab +bc + ca)) -------- (i) (a + b +c)^2= a^2+b^2+c^2+ 2(ab +bc + ca) 52= a^2+b^2+ c^2+ 30 25 - 30 = a^2+ b^2+ c^2 - 5 = a^2+b^2+ c^2 Putting the values in equation (i) we get = 2(5)(-5 - 15) = 2(5)(-20) = - 200 Ans: - 200

\left. \begin{array} { l } { \text { if } a + b + c = 5 \text { and } a b + b c + c a = 15 \text { find the valu } } \\ { ( a + b ) ^ { 3 } + ( b + c ) ^ { 3 } + ( c + a ) ^ { 3 } - 3 ( a + b ) ( b + c ) ( c + a ) } \end{array} \right.

Answer»

(a + b)^3+ (b +c)^3+ (c + a)^3- 3(a + b)(b +c)(c + a) = 2a^3+ 2b^3+2c^3- 6abc

2a^3+ 2b^3+ 2c^3- 6abc = 2(a^3+ b^3+c^3- 3abc) = 2(a + b+ c)(a^2+ b^2+c^2- (ab +bc + ca)) -------- (i)

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

52= a^2+b^2+ c^2+ 30

25 - 30 = a^2+ b^2+ c^2

- 5 = a^2+b^2+ c^2

Putting the values in equation (i) we get

= 2(5)(-5 - 15)

= 2(5)(-20) = - 200

Ans: - 200