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
Durgendra , 7 Years ago
Grade 11
10 grade maths> If x + y = 5xy, y + z = 6yz, z + x = 7zx ...
1 Answers
Arun
Last Activity: 7 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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