If a, b, c are the sides of a triangle ABC, then \({a^{\frac{1}{p}}} + {b^{\frac{1}{p}}} - {c^{\frac{1}{p}}}\) where p > 1, is
always positive
Concept:
- The triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
Calculation:
Given: a, b, c are the sides of a triangle ABC
Since a, b, c are positive numbers.
⇒ a1/p, b1/p, c1/p are positive numbers. ...(∵ p > 1)
We know that the sum of any two sides must be greater than the third side.
⇒ a1/p + b1/p > c1/p
⇒ a1/p + b1/p - c1/p > 0
∴ Option 2 is correct.
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