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Substitution Method to Remove Indeterminate Form

if a=2+ rad...

Question

if a=2+√3 prove that a²-4a+1=0

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Solution

$Dear Student, a = 2 + \sqrt{3} a^{2} - 4 a + 1 = 0 {(2 + \sqrt{3})}^{2} - 4 (2 + \sqrt{3}) + 1 = 4 + 3 + 4 \sqrt{3} - 8 - 4 \sqrt{3} + 1 = 0 Regards$

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A = (\begin{matrix} 1 & - 1 2 & 3 \end{matrix})

, then show that

A^{2} - 4 A + 5 I_{2} = 0

A

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦

, then prove that

A^{2} - 4 A - 5 I = 0

A = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 \end{matrix} ∣ ∣ ∣ ∣

, then prove that

A^{2} - 4 A - 5 I_{3} = 0

and hence obtain

A^{- 1}

A = [\begin{matrix} 1 & - 1 2 & 3 \end{matrix}]

, then prove that

A^{2} - 4 A + 5 I = 0

I

is a unitary matrix.

A = [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{matrix}]

A^{- 1}

A^{2} - 4 A - 5 I = O

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