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Question
If x : y = y : z, then x2 : y2 is ______.
Options
1 : x
x : y
x : z
z : x
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Solution
If x : y = y : z, then x2 : y2 is x : z.
Explanation:
Given x : y = y : z
`\implies x/y = y/z`
`\implies` y2 = xz ...(1)
∴ x2 : y2 = x2 : xz ...[Using (1)]
= `(x^2)/(xz)`
= `x/z`
= x : z
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