Question

A B C D are in continued proportion. $A^{2} +C^{2} =328$ , $D^{2} -B^{2} =2880$
Then find the value of $C^{2}D^{2}-A^{2} B^{2}$

Answer 1

Given :   A B C D are in continued proportion.    A²  + C²  = 328 ,   D² - B² = 2880

To find : C²D² - A²B²

Solution:

A : B : C : D

A/B = B/C = C/D  = k

=> A = Bk  , B = Ck  , C = Dk

A²  + C²  = 328

=> (Bk)² + (Dk)² = 328

=> k² ( B² + D)² = 328

C²D² - A²B²  

= (CD + AB)(CD  - AB)

= (DkD + BkB)(DkD - BkB)

= (D²k  + B²k) (D²k  - B²k)

= k(D² + B²)k(D² - B²)

= k²(D² + B²)(D² - B²)

= k² ( B² + D)² (D² - B²)

now using  D² - B² = 2880     & k² ( B² + D)² = 328

=  328 * 2880

=  944640

C²D² - A²B² = 944640

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