The average of a, b, c is 6 and a - b = 4, ab = 21; What is the value of c?
Solution
Correct Answer: Option C
Here, a + b + c = 3 × 6 = 18 ...... (i)
Again, (a + b)² = (a - b)² + 4ab
⇒ (a + b)² = (4)² + 4 × 21
⇒ (a + b)² = 16 + 84
⇒ (a + b)² = 100
⇒ a + b = 10
∴ (i) ⇒
10 + c = 18
⇒ c = 18 - 10
⇒ c = 8
Again, (a + b)² = (a - b)² + 4ab
⇒ (a + b)² = (4)² + 4 × 21
⇒ (a + b)² = 16 + 84
⇒ (a + b)² = 100
⇒ a + b = 10
∴ (i) ⇒
10 + c = 18
⇒ c = 18 - 10
⇒ c = 8
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