Quod Erat Demonstrandum

2012/09/20

To 4E students

Filed under: mathematics,NSS — johnmayhk @ 11:11 上午
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For Q.8, you may refer to

https://johnmayhk.wordpress.com/2008/11/16/f2-mathematics-factorization-by-cross-method/

For 0.5-mark questions,

Q.11

4x^3+x+1

\equiv 4x^3-x+2x+1

\equiv x(4x^2-1)+(2x+1)

\equiv x(2x+1)(2x-1)+(2x+1)

\equiv (2x+1)(x(2x-1)+1)

\equiv (2x+1)(2x^2-x+1)

Q.12

5x^2+2y^2-6xy+4x-2y+1=0

(x^2-2xy+y^2)+(4x^2-4xy+y^2)+4x-2y+1=0

(x-y)^2+(2x-y)^2+2(2x-y)+1=0

(x-y)^2+((2x-y)+1)^2=0

For x,y are real,

x-y=0
2x-y+1=0

On solving,

x=y=-1

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