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If A, B, C and Dare in Continued Proportion, Then Prove that - ICSE Class 10 - Mathematics

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Question

If a, b, c and dare in continued proportion, then prove that 

ad (c2 + d2) = c3 (b + d)

Solution

ad (c2 + d2) = c3 (b + d)

`"a"/"b" = "b"/"c" = "c"/"d" = "k"`

⇒ c = kd

b =kc= k2

a=kb=k3

ac( c2 + d2 ) = c3(b + d) 

LHS 

ac( c2 + d2

= k3d x c(k2 d2 + d2

= k3d3 (k2d + d) 

RHS 

c3(b + d) 

= k3d3(k2d + d) 

LHS = RHS. Hence , proved.

  Is there an error in this question or solution?

APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.3 | Q: 10.1

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Solution If A, B, C and Dare in Continued Proportion, Then Prove that Concept: Proportions.
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