If ac=cd=cf prove that : acbdcedfaedfa2b2+c2d2+e2f2=acbd+cedf+aedf - Mathematics

If `a/c = c/d = c/f` prove that : `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2) = "ac"/"bd" + "ce"/"df" + "ae"/"df"`

Sum

`a/c = c/d = c/f` = k(say)
∴ a = bk, c = dk, e =fk
L.H.S. = `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2)`

= `(b^2k^2)/(b^2) + (d^2k^2)/(d^2) + (f^2k^2)/(f^2)`
= k² + k² + k²
= 3k²
R.H.S. = `"ac"/"bd" + "ce"/"df" + "ae"/"bf"`

= `"bk.dk"/"b.d" + "dk.fk"/"d.f" + "bk.fk"/"b.f"`
= k² + k² + k²
= 3k²
∴ L.H.S. = R.H.S.

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Chapter 7: Ratio and Proportion - Exercise 7.2

Chapter 7 Ratio and Proportion
Exercise 7.2 | Q 17.3

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3 : 4 : : p : 12

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33, 121, 9, 96

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39 litres : 65 litres and 6 bottles : 10 bottles

If 4 : 5 : : x : 35, then the value of x is

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A gets double of what B gets and B gets double of what C gets. Find A : B and B : C and verify whether the result is in proportion or not

The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.