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erica [24]
2 years ago
13

How to do???????????​

Mathematics
1 answer:
Stella [2.4K]2 years ago
3 0

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

<em>p</em> = (10 + 2√5) / (1 - √5)²

and now you just simplify.

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

→   <em>p</em> = (10 + 2√5) / (6 - 2√5)

Cancel the common factor of 2 among all the terms:

<em>p</em> = (2•5 + 2√5) / (2•3 - 2√5)

→   <em>p</em> = (5 + √5) / (3 - √5)

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

<em>p</em> = (5 + √5) / (3 - √5) • (3 + √5) / (3 + √5)

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

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

→   <em>p</em> = (20 + 8√5) / 4

Cancel the factor of 4:

<em>p</em> = (4•5 + 4•2√5) / 4

→   <em>p</em> = 5 + 2√5

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