Solve this equation by completing squares
x2 - (√3 + 1 )x + √3=0
39We take the middle(x) coefficient, half it, then square it, and add and subtract it to the overall equation.
x² - (√3 + 1)x + (√3 + 1)²/4 - (√3 + 1)²/4 + √3 = 0
=> (x - (√3 + 1)2)² - (√3 + 1)²/4 + √3 = 0
=> (2x - (√3 + 1))² - (√3 + 1)² + 4√3 = 0
=> (2x - (√3 + 1))² - 3 - 1 - 2√3 + 4√3 = 0
=> (2x - (√3 + 1))² = 4 - 2√3
=> 2x - (√3 + 1) = ±√4 - 2√3
Yahan se nikal jaayega I guess. Do check for calc errors.
36by factorisation method
x2 - (√3 + 1 )x + √3 = 0
=> x2 - √3x - x + √3 = 0
=> x (x - √3) - 1( x - √3) = 0
=> (x - √3)(x - 1) = 0
=> x = √3 or x = 1
but do u think it is easy to find these values of x in
2x - (√3 + 1) = ±√4 - 2√3
apne ek chota sa step miss kar diya hai (which easily works out this prob)....!!
check out..!!
21yep its easy to find the values of x in
2x - (√3 + 1) = ±√(4-2√3)
because 4 - 2√3 = (√3 - 1)2