Question

solve:2(x+y)=xy, xy+yz+zx=108, xyz=180​

Answer 1

Given, x+y+z=8,xy+yz+zx=20

Now, x

3

+y

3

+z

3

−3xyz=(x+y+z)(x

2

+y

2

+z

2

−xy−yz−zx)

Again, (x+y+z)

2

=x

2

+y

2

+z

2

+2xy+2yz+2zx

x

2

+y

2

+z

2

=(x+y+z)

2

−2(xy+yz+zx)

x

2

+y

2

+z

2

=(8)

2

−2(20)=24

x

3

+y

3

+z

3

−3xyz=(x+y+z)[x

2

+y

2

+z

2

−(xy+yz+zx)]

x

3

+y

3

+z

3

−3xyz=(8)[24−(20)]

x

3

+y

3

+z

3

−3xyz=(8)[24−(20)]=8(4)=32

hope it helps you ☺️