If x:y = y:z = z:x,
prove that x + y + z = 0.
Originally posted by Achemtutor:If x:y = y:z = z:x,
prove that x + y + z = 0.
Question
If x:y = y:z = z:x,
prove that x + y + z = 0.
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x : y = y : z = z : x
x y z
--- = --- = ---
y z x
x y
From --- = ----
y z
y^2
x = ----
z
y z
From --- = ---
z x
z^2 = xy
y^2
Substitute x = ---- into z^2 = xy
z
y2
z^2 = ----- y
z
z ^3 = y^3
z = y
y^2
Substitute x = ---- and z = y into x + y + z
z
x + y + z
= y^2/z + y + z
= y^2/y + y + y
= 3y
For x + y + z = 0, y must be 0.
When y = 0, " x : y = y : z = z : x" will be correct only if x = 0 and z = 0.
But is the ratio of 0 : 0 a valid mathematical concept ? E.Maths students do not know the meaning of 0/0, the indeterminate form (L' Hospital Rule) is learnt only in the university.
For the question to be doable for the E.Maths students, x + y + z can be changed to 1, then the answers will be x = 1/3, y = 1/3, z = 1/3.
Achemtutor, you better stick to be a chemistry tutor lah.
Hi,
The question is not suited for E Maths. Thanks.
Cheers,
Wen Shih