If a, b and c are numbers that satisfy the conditions:

a + b + c = 20 and a^{2} + b^{2} + c^{2} = 200

Option 4 : 600

हिन्दी वर्णमाला सरल टेस्ट

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10 Questions
10 Marks
10 Mins

**Given:**

a + b + c = 20 and a^{2} + b^{2} + c^{2} = 200

**Concept used:**

**(**a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca)

**Calculation**:

**(**a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca)

⇒ (20)^{2} = 200 + 2(ab + bc + ca)

⇒(400 – 200) = 2(ab + bc + ca)

⇒ ab + bc + ca = 200 / 2

⇒(ab + bc + ca) = 100

**According to question –**

⇒ (a + b)^{2} + (a + c)^{2} + (b + c)^{2 }= a^{2} + b^{2} + 2ab + a^{2} + c^{2} + 2ac + b^{2} + c^{2 }+ 2bc

⇒ 2(a^{2} + b^{2} + c^{2}) + 2(ab + bc + ca)

⇒ 2(200) + 2(100)

⇒ 400 + 200

⇒ 600