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F. 2 Maths -Identities (最佳解答取40分)

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1. (a)Factorize a^4-2a^2b^2+b^4 (b)If a/b+b/a=2, find the value of a^4-2a^2b^2+b^4.2. It is given that y^2+1/y^2=7 and y=0, find the values of the following expressions.(a)y+1/y(b)(y-1/y)^2(c)(y^2-1/y^2)^2Remarks:1) Please show the working steps clearly. (2 points)2) Explain/state the working steps... 顯示更多 1. (a)Factorize a^4-2a^2b^2+b^4 (b)If a/b+b/a=2, find the value of a^4-2a^2b^2+b^4. 2. It is given that y^2+1/y^2=7 and y=0, find the values of the following expressions. (a)y+1/y (b)(y-1/y)^2 (c)(y^2-1/y^2)^2 Remarks: 1) Please show the working steps clearly. (2 points) 2) Explain/state the working steps in details. (2 points) 3) Make sure your answer is correct. (Total points of each question =4 points) -->5 X 4 X 2=40 points Thanks a lot!

最佳解答:

1(a) a^4-2a^2b^2+b^4 =(a^2-b^2)^2 (b) a/b+b/a=2 (a/b+b/a)^2 =4 (a^2/b^2)+(b^2/a^2)+2(a/b)(b/a) = 4 (a^2/b^2)+(b^2/a^2) = 2 (a^4+b^4)/(a^2b^2)=2 a^4+b^4=2a^2b^2 Therefore, a^4+b^4-2a^2b^2 = 0 2 Given that y^2+1/y^2=7 2(a) (y+1/y)^2 =y^2+2(y)(1/y)+(1/y^2 ) (y+1/y)^2 = 7+2 (y+1/y)^2 =9 y+1/y = 3 or -3 (rejected) Therefore, y+1/y =3 (b) (y-1/y)^2 = (y+1/y)^2-4y(1/y) = (3)^2 -4 = 9-4 =5 (c) Because (y-1/y)^2=5 y^2-2(y)(1/y)+(1/y^2) = 25 y^2-2+1/y^2 = 25 y^2+1/y^2 = 27 Also, (y^2-1/y^2)^2 = (y^2+1/y^2)^2-4(y^2)(1/y^2) = (27)^2-4 = 729-4 =725

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