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If xy+x+y =250, xz+x+z =300, yz+y+z =216, the find the value of x+y+z =?

If xy+x+y =250, xz+x+z =300, yz+y+z =216, the find the value of x+y+z =?

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Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
x+y+xy+1=251
(x+1)(y+1)=251
xz+x+z+1=301
(x+1)(z+1)=301
in same way
(y+1)(z+1)=217
now multiply all three
(x+1)(y+1)(z+1)))^2 =251 * 301 * 217
so (x+1)(y+1)(z+1)=sqrt(251) * sqrt(301) * sqrt(217)
now you have (x+1)(y+1) , you have (y+1)(z+1) , you have (x+1)(z+1) , you can find x,y,z & sum

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