Question

if a^2+b^2+c^2=280 and ab+bc+ca=9/2
then find the value of (a+b+c)^3​

Answer 1

Answer:

4913

Step-by-step explanation:

Given, a² + b² + c² = 280

and, ab + bc + ca = 9/2

Now, we know that,

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

→ 280 = (a + b + c)² - 2(9/2)

[since, a² + b² + c² = 280, and ab + bc + ca = 9/2]

→ 280 = (a + b + c)² - 9

→ (a + b + c)² = 280 + 9

→ (a + b + c)² = 289

→ (a + b + c)² = (17)²

→ a + b + c = 17

Now, we are asked for (a + b + c)³

So, (a + b + c)³ = 17³

→ (a + b + c)³ = 4913

Answer 2

Answer :-

4913

See the Attachment for Solution.