Question

Solve the equation
${x}^{2} - ( \sqrt{3} + 1)x + \sqrt{3 } = 0$
by the method of
completing the square.​

Answer 1

Answer:

x = (√3+1)+√(1+2√3) Or x = (√3+1)-√(1+2√3)

Step-by-step explanation:

x²-(√3+1)x+√3=0

=> x²-(√3+1)x = -√3

=> x² - 2×x × (√3+1)=-√3

=> x² -2×x×(√3+1)+(√3+1)²=-√3+(√3+1)²

=> [x-(√3+1)]² = -√3+√3+1+2√3

=> [x-(√3+1)]²=1+2√3

=> x-(√3+1)=±√(1+2√3)

=> x = (√3+1)±√(1+2√3)

Therefore,

x = (√3+1)+√(1+2√3) Or x = (√3+1)-√(1+2√3)

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