①若mn=53，则m2+2mn+n2m2−mn−2n2=．②若x3=y4=z5，则x2−3xy+2z23x2+2xy−z2=−526−526．③已知1a+1b=4，则4a+3ab+4b−3a+2ab−3b=−1910−1910．④若m+n=5，mn=3，则nm+mn=193193．

Question

①若(m)/(n)=(5)/(3)，则(m2+2mn+n2)/(m2−mn−2n2)=______．
②若(x)/(3)=(y)/(4)=(z)/(5)，则(x2−3xy+2z2)/(3x2+2xy−z2)=

−(5)/(26)

−(5)/(26)

．
③已知(1)/(a)+(1)/(b)=4，则(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(m)/(n)=(5)/(3)，则(m2+2mn+n2)/(m2−mn−2n2)=______．
②若(x)/(3)=(y)/(4)=(z)/(5)，则(x2−3xy+2z2)/(3x2+2xy−z2)=

−(5)/(26)

−(5)/(26)

．
③已知(1)/(a)+(1)/(b)=4，则(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(m)/(n)mmnn(5)/(3)，则(m2+2mn+n2)/(m2−mn−2n2)=______．
②若(x)/(3)=(y)/(4)=(z)/(5)，则(x2−3xy+2z2)/(3x2+2xy−z2)=

−(5)/(26)

−(5)/(26)

．
③已知(1)/(a)+(1)/(b)=4，则(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(5)/(3)5533(m2+2mn+n2)/(m2−mn−2n2)=______．
②若(x)/(3)=(y)/(4)=(z)/(5)，则(x2−3xy+2z2)/(3x2+2xy−z2)=

−(5)/(26)

−(5)/(26)

．
③已知(1)/(a)+(1)/(b)=4，则(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(m2+2mn+n2)/(m2−mn−2n2)m2+2mn+n2m2+2mn+n2m2+2mn+n2m2+2mn+n22+2mn+n2n2n22m2−mn−2n2m2−mn−2n2m2−mn−2n2m2−mn−2n22−mn−2n2n2n22
(x)/(3)=(y)/(4)=(z)/(5)，则(x2−3xy+2z2)/(3x2+2xy−z2)=

−(5)/(26)

−(5)/(26)

．
③已知(1)/(a)+(1)/(b)=4，则(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(x)/(3)xx33(y)/(4)=(z)/(5)，则(x2−3xy+2z2)/(3x2+2xy−z2)=

−(5)/(26)

−(5)/(26)

．
③已知(1)/(a)+(1)/(b)=4，则(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(y)/(4)yy44(z)/(5)，则(x2−3xy+2z2)/(3x2+2xy−z2)=

−(5)/(26)

−(5)/(26)

．
③已知(1)/(a)+(1)/(b)=4，则(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(z)/(5)zz55(x2−3xy+2z2)/(3x2+2xy−z2)=

−(5)/(26)

−(5)/(26)

．
③已知(1)/(a)+(1)/(b)=4，则(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(x2−3xy+2z2)/(3x2+2xy−z2)x2−3xy+2z2x2−3xy+2z2x2−3xy+2z2x2−3xy+2z22−3xy+2z2z2z223x2+2xy−z23x2+2xy−z2x2+2xy−z2x2+2xy−z22+2xy−z2z2z22

−(5)/(26)

−(5)/(26)(5)/(26)552626

−(5)/(26)

−(5)/(26)(5)/(26)552626
(1)/(a)+(1)/(b)=4，则(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(1)/(a)11aa(1)/(b)=4，则(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(1)/(b)11bb(4a+3ab+4b)/(−3a+2ab−3b)=

−(19)/(10)

−(19)/(10)

．
④若m+n=5，mn=3，则(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(4a+3ab+4b)/(−3a+2ab−3b)4a+3ab+4b4a+3ab+4b−3a+2ab−3b−3a+2ab−3b

−(19)/(10)

−(19)/(10)(19)/(10)19191010

−(19)/(10)

−(19)/(10)(19)/(10)19191010
(n)/(m)+(m)/(n)=

(19)/(3)

(19)/(3)

．(n)/(m)nnmm(m)/(n)=

(19)/(3)

(19)/(3)

．(m)/(n)mmnn

(19)/(3)

(19)/(3)(19)/(3)191933

(19)/(3)

(19)/(3)(19)/(3)191933

Answer 1

①m2+2mn+n2m2−mn−2n2＝(mn)2+2mn+1(mn)2−mn−2=(53)2+2×53+1(53)2−53−2=-8；②令x3＝y4＝z5＝k，则x=3k，y=4k，z=5k，所以x2−3xy+2z23x2+2xy−z2=(3k)2−3×3k×4k+2×(5k)23×(3k)2+2×3x×4k−(5k)2＝−5k...