F1.maths MC－utefdxd的部落格

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F1.maths MC

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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 .

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