If x2 - 1, 2x and x2 + 1 are the three sides of a right angled triangle, then which of the following can be its hypotenuse?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. x2 + 1.
Sum of the squares of the other two sides is equal to thw square of the hypotenuse.
Now, let x2 + 1 be the hypotenuse.
Then, (2x)2 + (x2 - 1)2 = 4x2 + x4 - 2x2 + 1
⇒ x4 + 2x2 + 1 = (x2 + 1)2
Hence proved.