Question

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If x/y+z + y/z+x + z/x+y = 1, then find the value of x²/y+z + y²/z+x + z²/x+y​

Answer 1

x²/y+z + y²/z+x + z²/x+y = 0

Step-by-step explanation:

x/y+z + y/z+x + z/x+y = 1

• Multiplying (x+y+z) both side

x(x+y+z)/y+z + y(x+y+z)/z+x + z(x+y+z)/x+y = (x+y+z)

x²+x(y+z)/y+z + y²+y(x+z)/z+x + z²+z(x+y)/x+y = (x+y+z)

x²/y+z +x + y²/z+x + y + z²/x+y + z = x+y+z

x²/y+z + y²/z+x + z²/x+y = x + y + z - x - y - z

x²/y+z + y²/z+x + z²/x+y = 0

__Hence Solved

Answer 2

Answer:

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x²/y+z + y²/z+x + z²/x+y = 0

Step-by-step explanation:

x/y+z + y/z+x + z/x+y = 1

• Multiplying (x+y+z) both side

x(x+y+z)/y+z + y(x+y+z)/z+x + z(x+y+z)/x+y = (x+y+z)

x²+x(y+z)/y+z + y²+y(x+z)/z+x + z²+z(x+y)/x+y = (x+y+z)

x²/y+z +x + y²/z+x + y + z²/x+y + z = x+y+z

x²/y+z + y²/z+x + z²/x+y = x + y + z - x - y - z

x²/y+z + y²/z+x + z²/x+y = 0

__Hence Solved___