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Question
If x, y, z are in continued proportion then `(x^2 + y^2)/(y^2 + z^2)` is equal to ______.
Options
`x/z`
`x/y`
`y/z`
`y/x`
MCQ
Fill in the Blanks
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Solution
If x, y, z are in continued proportion then `(x^2 + y^2)/(y^2 + z^2)` is equal to `bb(x/z)`.
Explanation:
If x, y, z are in continued proportion then,
`x/y = y/z`
y2 = xz
Substitute y2 = xz into the expression:
`(x^2 + y^2)/(y^2 + z^2)`
= `(x^2 + xz)/(xz + z^2)`
= `(x(x + z))/(z(x + z))`
= `x/z`
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