Question

How to do???????????​

Answer 1

The point (1 - √5, p) lies on the given curve, which means if x = 1 - √5, then y = p. So

p = (10 + 2√5) / (1 - √5)²

and now you just simplify.

(1 - √5)² = 1² - 2√5 + (√5)² = 6 - 2√5

→   p = (10 + 2√5) / (6 - 2√5)

Cancel the common factor of 2 among all the terms:

p = (2•5 + 2√5) / (2•3 - 2√5)

→   p = (5 + √5) / (3 - √5)

Multiply the numerator and denominator by the conjugate of the denominator:

p = (5 + √5) / (3 - √5) • (3 + √5) / (3 + √5)

→   p = ((5 + √5) (3 + √5)) / (3² - (√5)²)

→   p = (15 + 8√5 + (√5)²) / (3² - (√5)²)

→   p = (20 + 8√5) / 4

Cancel the factor of 4:

p = (4•5 + 4•2√5) / 4

→   p = 5 + 2√5