Question

If a+b+c=8 ab+bc+ca=15 then find the value of a3+b3+c3-3abc

Answer 1

We have the formula
a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ac)

we can write it as
a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - (ab + bc + ac))
Now we have
a + b + c = 8
ab + bc + ac = 15

Putting values we get
a³ + b³ + c³ - 3abc = 8(a² + b² + c² - 15)....(1)

Now, we also know that
(a + b + c)² = a² + b² + c² + 2(ab + bc + ac)
Putting values we get
8² = a² + b² + c² + 2(15)

a² + b² + c² = 64 - 30

a² + b² + c² = 34

Putting this in (1), we get
a³ + b³ + c³ - 3abc = 8(34 - 15)

a³ + b³ + c³ - 3abc = 8(19)
a³ + b³ + c³ - 3abc = 152

Answer 2

Answer:

Step-by-step explanation:

We have the formula

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

we can write it as

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

Now we have

a + b + c = 8

ab + bc + ac = 15

Putting values we get

a³ + b³ + c³ - 3abc = 8(a² + b² + c² - 15)....(1)

Now, we also know that

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

Putting values we get

8² = a² + b² + c² + 2(15)

a² + b² + c² = 64 - 30

a² + b² + c² = 34

Putting this in (1), we get

a³ + b³ + c³ - 3abc = 8(34 - 15)

a³ + b³ + c³ - 3abc = 8(19)

a³ + b³ + c³ - 3abc = 152