If a and b are the roots of the equation 2x^2-2x-5=0, find the value of a^2+b(1-a)
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F.4 Quadratic Equation
2012-09-16 7:45 pm
回答 (2)
2012-09-16 8:04 pm
✔ 最佳答案
a^2+b(1-a)=(2a+5)/2+b(1-a)
=a+5/2+b-ab
=(a+b)-ab+5/2
=-(-2)/2-(-5/2)+5/2
=6
2012-09-16 8:08 pm
a + b = 1 ...........(1)
ab = - 5/2 ............(2)
2a^2 - 2a - 5 = 0
so a^2 = (5 + 2a)/2 = 5/2 + a ........(3)
So a^2 + b(1 - a) = 5/2 + a + b - ab = 5/2 + 1 + 5/2 = 6.
ab = - 5/2 ............(2)
2a^2 - 2a - 5 = 0
so a^2 = (5 + 2a)/2 = 5/2 + a ........(3)
So a^2 + b(1 - a) = 5/2 + a + b - ab = 5/2 + 1 + 5/2 = 6.
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