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# Quadratics question - can you help me solve it? watch

1. Hi all. Okay so there's a line, and 3 lengths (a, b and c). Lengths a, b and c are on the same straight line. Length a is = to the length of the line. Length b is on the same line and is about 2/3 of the whole line. The remaining length of the line that isn't covered by b is the length of c.
The ratio of a : b is = to the ratio of b : c.

How can I show that this ratio is
( 1+ (√5) ) / 2 : 1

The length of b is not actually 2/3 of the line, I just wrote it to show what it would look like if you drew the lines.

Thank you guys.
2. (Original post by ZakA 42)
Hi all. Okay so there's a line, and 3 lengths (a, b and c). Lengths a, b and c are on the same straight line. Length a is = to the length of the line. Length b is on the same line and is about 2/3 of the whole line. The remaining length of the line that isn't covered by b is the length of c.
The ratio of a : b is = to the ratio of b : c.

How can I show that this ratio is
( 1+ (√5) ) / 2 : 1

The length of b is not actually 2/3 of the line, I just wrote it to show what it would look like if you drew the lines.

Thank you guys.
Moving to Maths

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3. (Original post by ZakA 42)
Hi all. Okay so there's a line, and 3 lengths (a, b and c). Lengths a, b and c are on the same straight line. Length a is = to the length of the line. Length b is on the same line and is about 2/3 of the whole line. The remaining length of the line that isn't covered by b is the length of c.
The ratio of a : b is = to the ratio of b : c.

How can I show that this ratio is
( 1+ (√5) ) / 2 : 1

The length of b is not actually 2/3 of the line, I just wrote it to show what it would look like if you drew the lines.

Thank you guys.
Have a look at the golden ratio and how it's calculated, it should help with your question.

The golden ratio is 'φ' (phi), but I'll call it as I've yet to figure out how to write that.

The ratio of a : b is = to the ratio of b : c.
So a/b = b/c =

You're also given that a=b+c.

So, subbing that into a/b, you get (b+c)/b. Dividing through by b, you get 1 + (c/b) = b/c = .

This gives you 1+()^-1 = . Can you take it from there?
4. (Original post by ZakA 42)
Hi all. Okay so there's a line, and 3 lengths (a, b and c). Lengths a, b and c are on the same straight line. Length a is = to the length of the line. Length b is on the same line and is about 2/3 of the whole line. The remaining length of the line that isn't covered by b is the length of c.
The ratio of a : b is = to the ratio of b : c.

How can I show that this ratio is
( 1+ (√5) ) / 2 : 1

The length of b is not actually 2/3 of the line, I just wrote it to show what it would look like if you drew the lines.

Thank you guys.
Let b=1

Now you have a:1 = 1:c
Giving 1:1/a = 1:c

So you have 1/a = c
And you know that c+1 = a

Solve for a

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Updated: January 8, 2015
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