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How to do???????????​

How to do???????????​-example-1

1 Answer

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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

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