rll33xb99t的部落格

標題:

中二數學問題 (20 分) !!~~ 急急急 ~~

發問:

(請列明步驟,並要用perfect square) 1.k^2 + 16k + 64 2.c^2 - 6c + 9 3.t^2 - 14t + 49 4.z^2 + 20yz + 100y^2 5.12m^2 + 12m + 3 6.80r ^2 + 40rs + 5s^2 7.(c - d)^2 + 4(c - d) + 4 8.1 - 6t^2 + 9t^4 - 121s^2 9.w^4 + 18w^2x^2 + 81x^4

最佳解答:

1.k^2 + 16k + 64 =k^2 +2(8)k + 8^2 =(k + 2) ^ 2 2.c^2 - 6c + 9 =c^2 - 2(3)c + 3^2 =(c - 3)^2 3.t^2 - 14t + 49 =t^2 - 2(7)t + 7^2 =(t-7)^2 4.z^2 + 20yz + 100y^2 =z^2 + 2(10y)z + (10y)^2 =(z+10y)^2 5.12m^2 + 12m + 3 =3[(2m)^2 + 2(2m)1 + 1^2] =3(2m+1)^2 6.80r ^2 + 40rs + 5s^2 =5[(4r) ^2 + 2(4r)s + s^2] =5(4r+s)^2 7.(c - d)^2 + 4(c - d) + 4 =(c - d)^2 + 2(c - d)2 + 2^2 =[(c - d)+2]^2 =(c - d+2)^2 8.1 - 6t^2 + 9t^4 - 121s^2 =(9t^4- 6t^2+1) - 121s^2 =[(3t^2)^2-2(3t^2)1+1^2]-(11s)^2 =(3t^2-1)^2-(11s)^2 =[(3t^2-1)-(11s)][(3t^2-1)+(11s)] =(3t^2-11s-1)(3t^2+11s-1) 9.w^4 + 18w^2x^2 + 81x^4 =(w^2)^2 + 2(w^2)(9x^2) + (9x^2)^2 =[w^2 + (3x)^2]^2

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其他解答:

1.k^2 + 16k + 64 =(k+8)^2 2.c^2 - 6c + 9 =(c-3)^2 3.t^2 - 14t + 49 =(t-7)^2 4.z^2 + 20yz + 100y^2 =(z+10)^2 5.12m^2 + 12m + 3 =3(4m^2+4m+1) =3(2m+1)^2 6.80r ^2 + 40rs + 5s^2 =5(16r^2+8rs+s^2) =5(4r+s)^2 7.(c - d)^2 + 4(c - d) + 4 =[(c-d)+4)]^2 =(c-d+4)^2 9. w^4 + 18w^2x^2 + 81x^4 =(w^2+9x^2)^2 2007-10-23 19:43:45 補充： 8.1 - 6t^2 + 9t^4 - 121s^2=(9t^4- 6t^2+1) - 121s^2=[(3t^2)^2-2(3t^2)1+1^2]-(11s)^2=(3t^2-1)^2-(11s)^2=[(3t^2-1)-(11s)][(3t^2-1)+(11s)]=(3t^2-11s-1)(3t^2+11s-1)