Question

Rozwiąż podane równanie metodą rozkładu na czynniki x2=3

2x2-5=0

x2+10x+25=0

x2+3=2^3x

Answer 1

x^2 = 3

x^2 - 3 = 0

( x - p(3))*( x + p(3)) = 0

x = p(3)  lub x = - p(3)

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p(3) - pierwiastek kwadratowy z 3

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2 x^2 - 5 = 0  / : 2

x^2 - 5/2 = 0

( x - p(5/2))*( x + p(5/2)) = 0

x = p(5/2)   lub  x = - p(5/2)

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x^2 + 10 x + 25 = 0

( x + 5)^2 = 0

x + 5 = 0

x = - 5

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x^2 +3 = 8 x

x^2 - 8 x + 3 = 0

delta = ( -8)^2 - 4*1*3 = 64 - 12 = 52 = 4*13

p (delty) = 2 p(13)

x1 = [ 8 - 2 p(13)]/2 = 4 - p(13

x2 = [ 8 + 2 p(13)]/2 = 4 + p(13)

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