How to solve complex Simultaneous Linear Equations Find a and b (1) a [ (

fulgoripb0b

fulgoripb0b

Answered question

2022-06-04

How to solve complex Simultaneous Linear Equations
Find a and b
(1) a [ ( 1 + 5 ) / 2 ] + b [ ( 1 5 ) / 2 ] = 1
(2) a [ ( 1 + 5 ) / 2 ] 2 + b [ ( 1 5 ) / 2 ] 2 = 2
Is there a smart method to solve this Simultaneous Linear Equations ?

Answer & Explanation

daman375ve6xe

daman375ve6xe

Beginner2022-06-05Added 2 answers

Write φ = 1 + 5 2 , so that
1 5 2 = 1 φ
and your system becomes
{ φ a + ( 1 φ ) b = 1 φ 2 a + ( 1 φ ) 2 b = 2
Multiply the first equation by 1 ϕ and subtract; now
a ( φ ( 1 φ ) φ 2 ) = 1 φ 2
shouldn't be difficult to solve.
Angeline Henderson

Angeline Henderson

Beginner2022-06-06Added 1 answers

Let α = 1 + 5 2 , β = 1 5 2 . Since we have α 2 = 1 + α , β 2 = 1 + β ,, we have a ( 1 + α ) + b ( 1 + β ) = 2.
Then, you can get a + b = 1.

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