1) 5x2 - 11x + 2 = 02) 6x2 - x - 15 = 03) 7x2 - x - 6 = x(x - 6)4) 3x(x2 - 2x) - x2(x +...

Question

1) 5x2 - 11x + 2 = 0
2) 6x2 - x - 15 = 0
3) 7x2 - x - 6 = x(x - 6)
4) 3x(x2 - 2x) - x2(x + 1) = 2x3 - 6x - 1

Answer 1

1) 5X^2 - 11X + 2 = 0
D = 121 - 40 = 81 ;√ D = 9
X1 = ( 11 + 9 ) : 10 = 2 
X2 = ( 11 - 9 ) : 10 = 0,2 
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2) 6X^2 - X - 15 = 0 
D = 1 + 360 = 361 ; √ D = 19 
X1 = ( 1 + 19 ) : 12 = 5/3 = 1 2/3 
X2 = ( 1 - 19 ) : 12 = - 18/12 = - 1,5 
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3) 7X^2 - X - 6 = X*( X - 6) 
7X^2 - X - 6 = X^2 - 6X 
7X^2 - X^2 - X + 6X - 6 = 0 
6X^2 + 5X - 6 = 0
D = 25 + 144 = 169 ; √ D = 13
X1 = ( - 5 + 13 ) : 12 = 8/12 = 2/3 
X2 = ( - 5 - 13 ) : 12 = - 18/12 = - 1,5 
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4) 3X*( X^2 - 2X) - X^2 *( X + 1 ) = 2X^3 - 6X - 1 
3X^3 - 6X^2 - X^3 - X^2 = 2X^3 - 6X - 1 
2X^3 - 7X^2 = 2X^3 - 6X - 1 
7X^2 - 6X - 1 = 0
D = 36 + 28 = 64 ; √ D = 8
X1 = ( 6 + 8) : 14 = 1
X2 = ( 6 - 8) : 14 = - 2/14 = - 1/7