Question

If x=(√5+1)/(√5-1) and y=(√5-1)/(√5+1) Find the value of x^2+y^2

Please answer my question...i will give you 50 points.....

Answer 1

given, x = (√5 + 1)/(√5 - 1) and y = (√5 - 1)/(√5 + 1)

rationalising x and y,

x = (√5 + 1)/(√5 - 1) × (√5 + 1)/(√5 + 1)

= (√5 + 1)²/(√5² - 1²)

= (5 + 1 + 2√5)/4

= (3 + √5)/2

similarly, y = (√5 - 1)/(√5 + 1) × (√5 - 1)/(√5 - 1)

= (√5 - 1)²/(√5² - 1²)

= (5 + 1 - 2√5)/2

= (3 - √5)/2

so, x² + y² = [(3 + √5)/2]² + [(3 - √5)/2]²

= (3 + √5)²/4 + (3 - √5)²/4

= {(3 + √5)² + (3 - √5)²}/4

= {3 + 5 + 6√5 + 3 + 5 - 6√5}/4

= (3 + 5 + 3 + 5)/4

= 16/4 = 4

hence, x² + y² = 4

Answer 2

See the attachment which I attached.