Question

Hypotenuse= 1 + x²
Perpendicular= 2x

Find Base using Pythagoras theorem!
(line by line)​

Answer 1

Step-by-step explanation:

H² = p² + b²

=> b² = H² - p² = (1+x²)² - (2x)² = 1+ x⁴ + 2x² - 4x²

= x⁴ - 2x² + 1 = (x²-1)²

=> b = x²-1

Answer 2

Give Hypotenus =1+x²

Perpendicular = 2x

According to the Pythagorean theorem

H² = P² + B² where

H= Hypotenus

B= Base

P = Perpendicular

( 2x ) ² + B² = (1+x²)²

4x² + B² = 1 + x⁴ + 2x². [ (a+b)² = a²+ b² + 2ab ]

4x²- 2x² + B² = 1 + x⁴

2x² + B² = 1 + x⁴

B² = x⁴ + 2x² + 1

B² = x⁴ + 1x² + 1x² + 1

B² = x² ( x² + 1 ) + 1 ( x²+1 )

B² = ( x² + 1 )( x²+1)

B = √ (x²+1)²

B = ( x²+1 ) /( x²-1)