Toán Lớp 7: Tính M=X+y+z biết 13/X+y +13/y+z +13/z+X=11z/X+y +11X/y+z + 11z/z+X=143/10

Question

Toán Lớp 7:  Tính M=X+y+z biết 13/X+y +13/y+z +13/z+X=11z/X+y +11X/y+z + 11z/z+X=143/10

huenthanh97 · Answer

$  $   13/(x+y) +(13)/(y+z) + (13)/(z+x) = 143/10   -> 13 (1/(x+y)+1/(y+z) +1/(z+x) ) = 143/10   -> 1/(x+y)+1/(y+z)+1/(z+x)=143/10 : 13   -> 1/(x+y)+1/(y+z)+1/(z+x)=11/10   $  $   (11z)/(x+y)+(11x)/(y+z)+(11y)/(z+x)=143/10   -> ( (11z)/(x+y)+(11x)/(y+z)+(11y)/(z+x) ) . 1/11= 143/10 . 1/11   -> z/(x+y)+x/(y+z)+y/(z+x) = 13/10   -> z/(x+y)+x/(y+z)+y/(z+x) +3=13/10 + 3   -> ( z/(x+y)+1) + ( x/(y+z)+1) + (y/(z+x)+1)=43/10   -> ( z/(x+y)+(x+y)/(x+y) ) + (x/(y+z)+(y+z)/(y+z) ) + (y/(z+x)+(z+x)/(z+x) ) = 43/10   ->(x+y+z)/(x+y) + (x+y+z)/(y+z) + (x+y+z)/(z+x) = 43/10   -> (x+y+z) (1/(x+y)+1/(y+z)+1/(z+x) ) = 43/10   -> (x+y+z) . 11/10 = 43/10   -> x+y+z=43/10 : 11/10   ->x+y+z=43/11   Vậy x+y+z=43/11

ngoclandiep · Answer

Giải đáp: $x+y+z= dfrac{43}{11}$   Lời giải và giải thích chi tiết:   Ta c&oacute;:   $ dfrac{11z}{x+y}+ dfrac{11x}{y+z}+ dfrac{11y}{z+x}= dfrac{143}{10}$   $ to  dfrac{z}{x+y}+ dfrac{x}{y+z}+ dfrac{y}{z+x}= dfrac{13}{10}$   $ to (1+ dfrac{z}{x+y})+(1+ dfrac{x}{y+z})+(1+ dfrac{y}{z+x})=3+ dfrac{13}{10}$   $ to  dfrac{x+y+z}{x+y}+ dfrac{x+y+z}{y+z}+ dfrac{x+y+z}{z+x}= dfrac{43}{10}$   $ to (x+y+z)(  dfrac{1}{x+y}+ dfrac{1}{y+z}+ dfrac{1}{z+x})= dfrac{43}{10}$   Lại c&oacute;:   $ dfrac{13}{x+y}+ dfrac{13}{y+z}+ dfrac{13}{z+x}= dfrac{143}{10}$   $ to  dfrac{1}{x+y}+ dfrac{1}{y+z}+ dfrac{1}{z+x}= dfrac{11}{10}$   $ to (x+y+z) cdot  dfrac{11}{10}= dfrac{43}{10}$   $ to x+y+z= dfrac{43}{11}$