Question

if a+b+c=15,ab+bc+ca=83,find a³+b³+c³-3abc​

Answer 1

Answer:

∴ a³+b³+c³-3abc = -360

Step-by-step explanation:

Given,

a+b+c = 15

ab+bc+ca = 83

a³+b³+c³-3abc = ?

Now,

a³+b³+c³-3ac

= (a+b+c)(a²+b²+c²-ab-bc-ca)

= 15[{(a+b+c)²-2ab-2bc-2ca}-(ab+bc+ca)]

= 15[(15)²-2(ab+bc+ca)-83]

= 15(225-2×83-83)

= 15(225-166-83)

= 15×(-24)

= -360

I hope this is the correct answer.