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.
Important Questions from Properties of Triangles
What is the value of a + b + √2 c equal to ?
What is the perimeter of the triangle ?
Consider the following statements :
1. ABC is right angled triangle
2. The angles of the triangle are in AP
Which of the statements given above is/are correct ?
What is the nature of the triangle ?
If c = 8, what is the area of the triangle ?
