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If x + y = 5xy, y + z = 6yz, z + x = 7zx find the value of x + y + z

 If x + y = 5xy, y + z = 6yz, z + x = 7zx find the value of x + y + z

Grade:11

1 Answers

Arun
25763 Points
3 years ago

x + y = 5xy  Multiply both sides by z

xz + yz = 5xyz

y + z = 6yz Multiply bth sides by x

xy  +xz = 6xyz

z + x = 7zx Multiply both sides by y

zy + xy =7xyz

xz + yz + xy + xz + zy + xy = 18xyz

2(xy + yz + xz) = 18xyz

xy + yz + xz = 9xyz

xy + z(y  + x) = 9xyz

xy + z(5xy) = 9xyz

xy = 4xyz

1 = 4z

z = 1 / 4  , x =1 / 3 , y = 1 / 2

Value of x + y + z = 1 / 4 + 1 / 3 + 1 / 2 = 13 / 12

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