Question

The diagram shows a right-angled triangle. Show that x²-4x-20=0

Answer 1

Step-by-step explanation:

By Pythagoras theorem

$(x + 5) {}^{2} = {(x + 1)}^{2} + {(x + 2)}^{2} \\ {x}^{2} + 25 + 10x = {x}^{2} + 1 + 2x + {x}^{2} + 4 + 4x \\ {x}^{2} + 25 + 10x = 2 {x}^{2} + 6x + 5 \\ 0 = 2 {x}^{2} - {x}^{2} + 6x - 10x + 5 - 25 \\ 0 = {x}^{2} - 4x - 20$

Answer 2

Answer:

proof in the attachment

Step-by-step explanation: