Question

Q-13 If a+b+c=9 and ab+bc+ca=40, find a2+b2+c2?​

Answer 1

Given, a + b + c = 9 and ab + bc + ca = 40

We know that,

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

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

⇒ a² + b² + c² = (9)² – 2 × 40 = 81 – 80 = 1 [a + b + c = 9 and ab + bc + ca = 40]

Thus, the value of a² + b² + c² is 1 .

Answer 2

Step-by-step explanation:

Given

• a + b + c = 9
• ab + bc + ca = 40

Find

• a² + b² + c²

We know that

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

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

→ (9) ² - 2 ( ab + bc + ca ) = a² + b² + c²

→ 81 - 2*40 = a² + b² + c²

→ 81 - 80 = a² + b² + c²

→ a² + b² + c² = 1