if
ab + bc + ca = 10 and a^2 + b^2 + c^2=44 find a^3 + b^3 + c^3-3 abc
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Answered by
0
Answer:
272
Step-by-step explanation:
Given: ab + bc + ca = 10 and a^2+b^2 +c^2 = 44
(a+b+c)^2 = a^2 +b^2+c^2+2(ab+bc+ca)
= 44 + 2(10)
= 44 + 20 = 64
a+b+c. = √64 = 8
a^3 + b^3 +c^3 - 3abc = (a+b+c) (a^2+b^2+c^2 -ab -bc - ca )
= (8)(44-10)=8(34)=272
Answered by
1
Answer:
(a+b+c)³=(a³+b³+c³)+3[(a+b+c)(ab+ac+bc)−abc]
(a+b+c)³ = (a³+b³+c³) + 3(10)(a+b+c) -3abc
(a³+b³+c³) - 3abc = (a+b+c)³ - 30(a+b+c)
(a³+b³+c³) - 3abc = (a+b+c) [ (a+b+c)^2 - 30 ]
(a³+b³+c³) - 3abc = (a+b+c) [ 44 +10 -30 ]
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