00:00In this question, we are given P, Q, and R are 3 unequal numbers, P, Q, and R are in
00:04A, P, and Q minus P, R minus Q, and P are in J, P, and we have been asked
00:11the value of this gesture.
00:13So, first of all, we can assume P, Q, R to be A minus D, A, A plus D.
00:19You can see the common difference between these is B.
00:22We can also assume them in the standard form A, A plus D, A plus 2D.
00:29But, this simplifies the equation and makes it easier to calculate and also saves our time.
00:35So, now we will put the value in this one.
00:38They are in G, P.
00:40So, Q minus, in G, P, there is the identity.
00:43The common ratio is same, which means P upon R minus Q is equal to R minus Q divided by
00:52Q minus P.
00:53So, we will put here, R minus Q divided by Q minus P is equal to P divided by R
00:59minus Q.
01:00As common ratio, this divided by this is common ratio, and common ratio is equal in G, P.
01:09Now, put the value from here.
01:11R value is A plus D minus Q value A.
01:15A plus D minus A is equal to D.
01:17In the same way, Q minus P, A minus A cancel, minus minus D.
01:25If we minus, and minus become plus, so this becomes plus D.
01:30In the same way, here, R minus Q, A plus D minus D.
01:37And, what else, P, P value is A minus D, we have put.
01:43From this two, D cancelled, A minus D is equal to D.
01:47A is equal to 2D.
01:49Now, simply put the values of in G.
01:52We put P value is A minus D.
01:56Q value is A.
01:57So, it becomes A minus D plus A, 2A minus D.
02:02Q plus R, Q plus R, Q plus R, 2A plus D, and R plus D, 2A.
02:10A minus D plus A plus D, minus 2 plus D, cancel, 2A.
02:15Now, put the value of A from this equation.
02:18A is equal to 2D.
02:20So, 4D minus D, 3D, 4D plus D, 5D, 4D.
02:26The 2D cancelled, so this ratio becomes 3 ratio, 5 ratio for final answer.
02:31Here comes the tensile Š³Š»Š°Š²an.
02:31Go ahead and see my Feat?
02:32Hi.
02:32Good.
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