Упростить и найти значение,если х＝1 у＝0.1 z＝0.01. Created by thbst. algebra-ru

Упростить и найти значение,если х＝1 у＝0.1 z＝0.01...

NNNLLL54

Verified answer

Ответ:

$x=1\ \ ,\ \ y=0,1\ \ ,\ \ z=0,01\\\\\\\dfrac{x^3y-xy^3+y^3z-yz^3+z^3x-zx^3}{x^2y-xy^2+y^2z-yz^2+z^2x-zx^2}=\dfrac{x^3(y-z)+y^3(z-x)+z^3(x-y)}{x^2(y-z)+y^2(z-x)+z^2(x-y)}=\\\\\\=\dfrac{1\cdot (0,1-0,01)+0,001(0,01-1)+0,000001(1-0,1)}{1\cdot 0,09+0,01\cdot (-0,99)+0,0001\cdot 0,9}=\\\\\\=\dfrac{0,09-0,00099+0,0000009}{0,09-0,0099+0,00009}=\dfrac{0,0890109}{0,08019}=\dfrac{890109}{801900}=1,11$

1 votes Thanks 1

nafanya2014

Verified answer

$\frac{x^3y-xy^3+y^3z-yz^3+z^3x-zx^3}{x^2y-xy^2+y^2z-yz^2+z^2x-xz^2} =\frac{xy(x^2-y^2)+yz(y^2-z^2)+xz(z^2-x^2)}{xy(x-y)+yz(y-z)+xz(z-x)} =$

$=\frac{xy(x^2-y^2)+yz(y^2-z^2)+xz(z^2-x^2+y^2-y^2)}{xy(x-y)+yz(y-z)+xz(z-x+y-y)} =\frac{xy(x^2-y^2)+yz(y^2-z^2)-xz(y^2-z^2)-xz(x^2-y^2)}{xy(x-y)+yz(y-z)-xz(x-y)-xz(y-z)} =$

$=\frac{(x^2-y^2)(xy-xz)+(y^2-z^2)(yz-xz)}{(x-y)(xy-xz)+(y-z)(yz-xz)} =\frac{x(x^2-y^2)(y-z)+z(y^2-z^2)(y-x)}{x(x-y)(y-z)+z(y-z)(y-x)} =$

$=\frac{x(x^2-y^2)(y-z)-z(y^2-z^2)(x-y)}{x(x-y)(y-z)-z(y-z)(x-y)} =\frac{(x-y)(y-z)(x^2+xy-zy-z^2)}{(x-y)(y-z)(x-z)}=\frac{x^2+xy-zy-z^2}{x-z}$

$=\frac{(x-z)(x+z)+y(x-z)}{x-z}=\frac{(x-z)(x+z+y)}{x-z}=x+z+y$

При x=1; y=0,1; z=0,01

получаем ответ:

1+0,1+0,01=1,11

1 votes Thanks 1

Answers & Comments

Verified answer

Verified answer

kak svyazat fajly html i css

elektronnij balans cao c cac2 co 4 al 3 c al4c3

matematika 11 klass114

pochemu v predlozhenii i wish it would stop snowing would a ne will

geometriya 11 klasa519626f63427eb9eb8304fc7e4dc383 46841

dlya yakih oblastej ukrayini harakterna najnizhcha gustota naselennya varianti vidpov

geometriya 11 klass7e08ff89dbe0335a17c72bdf21ae2c73 72358

anglijskijznayu chto otvet sno pochemu

caso3 4c cac2 3co

viznachte prirodnij pririst naselennya u promile yaksho vidomo sho za rik narodilos

рекомендуемые вопросы

Helpful Links

Helpful Social