Question

Find x 2 + y 2 for x = 3+ 2 3− 2 and y= 3− 2 3+ 2 . Using a reasoning, deduce that x 2 + y 2 will remain same even if values of x and y are interchanged.

Answer 1

Answer:

(x1,y1),(x2,y2),(x3,y3) lie on same line

To prove

x2x32−y3+x3x1y3−y1+x1x2y1−y2=0

Let the line be y=mx+c

(x1,y1) is on the line

⇒y1=mx1+c

(x2,y2) is on the line

⇒y2=mx2+c

(x3,y3