See hereI dont even get why one deserve to write (sqrt(5) + 1) / 2 - (1-sqrt(5) / 2 together ((sqrt(5) + 1) / 2 + (sqrt(5) - 1 ) / 2.

You are watching: (1-sqrt(5))/2 I dont also get why one can write (sqrt(5) + 1) / 2 - (1-sqrt(5) / 2 as ((sqrt(5) + 1) / 2 + (sqrt(5) - 1 ) / 2.

writing something as a - b is the very same as creating a + (-b). So in that action they simply multiply the second fraction by minus one (which efficiently multiplies each of the state in the molecule by minus one).

This whole collection of procedures is an extremely strange though.. The last step isn't even totally screenshotted and also I would more than likely make sure these two fractions re-publishing the same denominator first. IE:

(sqrt(5) + 1)/2 - (1 - sqrt(5)) / 2

= (sqrt(5) + 1 - (1 - sqrt(5))) / 2

Can you continue from here?

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level 1
· 1y
college mathematics instructor

Regarding your second question, do you think that a-(b-c) deserve to be rewritten together a-b+c or a+c-b?

Subtracting a sum is the same as adding the the opposite of every term in the sum.

10-(3+4) = 10 + (-3) + (-4)

10-(4-3) = 10 + (-4) + -(-3)

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· 1y · edited 1y
New User

I dont also get why one can write (sqrt(5) + 1) / 2 - (1-sqrt(5) / 2 as ((sqrt(5) + 1) / 2 + (sqrt(5) - 1 ) / 2.

The an adverse of a - b is b - a.

a - b is the same as a + (-b). Take the an adverse of that and you have actually (-a) + b i beg your pardon is the very same as b - a.

As for your topic line they're just looking at the numerator. Notification that it claims 1 + sqrt(5) - 1 + sqrt(5). That's simply the numerator. And also that simplifies to 2sqrt(5).

And that happens due to the fact that the sqrt(5) terms include and the 1's publication out.

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level 1
· 1y

the picture you post is a complete explanation of the concern you room asking. What don't girlfriend understand around it?

I dont also get why one have the right to write (sqrt(5) + 1) / 2 - (1-sqrt(5) / 2 as ((sqrt(5) + 1) / 2 + (sqrt(5) - 1 ) / 2.

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-(a-b) = b-a

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