If x . y . z = 1 show that 1 1 + x +...

Audrina Jackson

Audrina Jackson

Answered

2022-07-09

If x . y . z = 1 show that 1 1 + x + y 1 + 1 1 + y + z 1 + 1 1 + z + x 1 = 1
My attempt - L.H.S = 1 1 + x + y 1 + 1 1 + y + z 1 + 1 1 + z + x 1
= y y + x y + 1 + z z + y z + 1 + x x + z x + 1
= y z y z + x y z + z + z z + y z + 1 + x x + z x + 1
What to do next?

Answer & Explanation

pompatzz8

pompatzz8

Expert

2022-07-10Added 11 answers

1 1 + x + y 1 = y y + x y + 1 = y z y z + x y z + z (  multiplying by  z )
1 1 + x + y 1 = y z y z + 1 + z
1 1 + y + z 1 = z z + y z + 1 (  multiplying by  z )
1 1 + z + x 1 = x x + z x + 1 = x y z x y z + y z ( z x ) + y z (  multiplying by  y z )
1 1 + z + x 1 = 1 1 + z + y z
Augustus Acevedo

Augustus Acevedo

Expert

2022-07-11Added 4 answers

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

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