Question

if a+b+c =5 and ab+bc+ca =10 find a^3+b^3+c^3​

Answer 1

We know that,

a³ + b³ + c³ -3abc = (a + b + c )(a² + b² + c² -ab -bc-ca)

Finding a²+b²+c²,

(a + b + c)² = a² + b² + c² +2(ab+bc+ca)

(5)² -2×10 = a² + b² + c²

a²+b²+c² =5

a³+b³+c³-3abc=(5)(5-(ab+bc+ca)

a³+b³+c³-3abc=5(5-10)

=5(-5)

=-25

Answer 2

Step-by-step explanation:

a³ + b³ + c³ - 3abc =

(a + b + c)(a² + b² + c² - ab - bc - ca)

(a + b + c )² =

a² + b² + c² + 2ab + 2bc + 2ca

from second property we get

a² + b² + c² =

(a + b + c )² -2(ab + bc + ca)

by putting value we get

=25-20

=5

now these value putting in first formula

we get our answer

thank you