Question

if x²=√5+1/√5-1 then proved x²-x-1=0​

Answer 1

Step-by-step explanation:

x=[(5^1/2+1)/(5^1/2–1)]^1/2

Multiply above and below by(5^1/2+1)^1/2

x=(5^1/2+1)/2……………(1)

5x=(5/2).(5^1/2+1)………………(2)

squaring both sides eq.(1)

x^2=(5+1+2.5^1/2)/4=(6+2.5^1/2)/4

x^2=(3+5^1/2)/2

5.x^2=(5/2)(3+5^1/2)

5x^2+1=(5/2)(3+5^1/2)+1…………………….(3)

Subtract eq.(2) from eq.(3)

5x^2+1–5x=(5/2)(3+5^1/2)+1–(5/2)(5^1/2+1)

5x^2–5x+1=(5/2)(3+5^1/2–5^1/2–1)+1

5x^2–5x+1=5+1=6 , Answer

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