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F1.maths MC
發問:
The H.C.F and L.C.M of three algebraic expressions are x*z^2 and x^3*y^4*z^4 respectively. If two of the algebraic expressions are x^2*y^2*z^3 and x^3*y^4*z^2, find the third algebraic expression. A.x^3*z^3 B.x^2*y^4*z^2 C.x*y^4*z^4 D.x*z^4 我答左D,唔知岩唔岩 pleases explain~ 更新: 先次方後成除.thx
最佳解答:
您好，我是 lop，高興能解答您的問題。 Method 1 : If the third algebraic expression is A. (x^3)(z^3) , then the H.C.F. and L.C.M. of the three algebraic expressions will be (x^2)(z^2) and (x^3)(y^4)(z^3) respectively , not correct . If the third algebraic expression is B. (x^2)(y^4)(z^2) , then the H.C.F. and L.C.M. of the three algebraic expressions will be (x^2)(y^2)(z^2) and (x^3)(y^4)(z^3) respectively , not correct . If the third algebraic expression is C. (x)(y^4)(z^4) , then the H.C.F. and L.C.M. of the three algebraic expressions will be (x)(y^2)(z^2) and (x^3)(y^4)(z^4) respectively , not correct . If the third algebraic expression is D. (x)(z^4) , then the H.C.F. and L.C.M. of the three algebraic expressions will be (x)(z^2) and (x^3)(y^4)(z^4) respectively , correct . So the answer is D . Method 2 : The H.C.F. of the three algebraic expressions is (x)(z^2) , that means at least one of the algebraic expressions don't have the factor y . But the algebraic expressions (x^2)(y^2)(z^3) and (x^3)(y^4)(z^2) both have the factor y , so the third algebraic expression doesn't have the factor y . Only D. doesn't have the factor y . So the answer is D .
其他解答:
F1.maths MC
發問:
The H.C.F and L.C.M of three algebraic expressions are x*z^2 and x^3*y^4*z^4 respectively. If two of the algebraic expressions are x^2*y^2*z^3 and x^3*y^4*z^2, find the third algebraic expression. A.x^3*z^3 B.x^2*y^4*z^2 C.x*y^4*z^4 D.x*z^4 我答左D,唔知岩唔岩 pleases explain~ 更新: 先次方後成除.thx
最佳解答:
您好，我是 lop，高興能解答您的問題。 Method 1 : If the third algebraic expression is A. (x^3)(z^3) , then the H.C.F. and L.C.M. of the three algebraic expressions will be (x^2)(z^2) and (x^3)(y^4)(z^3) respectively , not correct . If the third algebraic expression is B. (x^2)(y^4)(z^2) , then the H.C.F. and L.C.M. of the three algebraic expressions will be (x^2)(y^2)(z^2) and (x^3)(y^4)(z^3) respectively , not correct . If the third algebraic expression is C. (x)(y^4)(z^4) , then the H.C.F. and L.C.M. of the three algebraic expressions will be (x)(y^2)(z^2) and (x^3)(y^4)(z^4) respectively , not correct . If the third algebraic expression is D. (x)(z^4) , then the H.C.F. and L.C.M. of the three algebraic expressions will be (x)(z^2) and (x^3)(y^4)(z^4) respectively , correct . So the answer is D . Method 2 : The H.C.F. of the three algebraic expressions is (x)(z^2) , that means at least one of the algebraic expressions don't have the factor y . But the algebraic expressions (x^2)(y^2)(z^3) and (x^3)(y^4)(z^2) both have the factor y , so the third algebraic expression doesn't have the factor y . Only D. doesn't have the factor y . So the answer is D .
其他解答:
此文章來自奇摩知識+如有不便請留言告知
x^2*y^2*z^3 x^3*y^4*z^2 呢2條式既 LCM: x^3*y^4*z^3 <<相同取最大指數 HCF: x^2*y^2*z^2 <<相同取最小指數 而再同 第3條式計LCM同HCF, 就會得出 LCM:x^3*y^4*z^4 HCF:x*z^2 LCM係拎最大指數, 咁姐係話第3條式一定有z^4, 先至有上面個個LCM HCF係拎最小指數, 姐係話第3條式一定有x,同埋冇y,先至有上面個個HCF (冇y可以睇作y^0) 咁所以個答案會有z^4,有x,冇y 所以答案係D|||||- the two algrebraic expression has Y but HCF does not include Y therefore no Y is in the third expression - in HCF, the power to X is 1 but the power to X in the two given expressions are 2 & 3 respectively therefore the power to x in the third expression should be 1 - in LCM, the power to Z is 4 but the power to Z in the two given expressions are 3 & 2 respectively therefore the power to Z in the third expression should be 4 so correct answer is D.
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