If one geometric mean G and two arithmetic mean A and B are inserted between two given quantities , then find (2A-B)(2B-A) a) 2G b) G C) G^2 d) G^3?

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If one geometric mean G and two arithmetic mean A & B are inserted between two given quantities , then find (2A-B)(2B-A) a) 2G b) G C) G^2 d) G^3?

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If one geometric mean G and two arithmetic mean A & B are inserted bet...

Let the two nos. Be a and b.

Geometric mean (G) between a and b will be √ab

G^2 = ab ---------(1)

Given : p and q are 2 arithmetic mean between a and b

Then A.P. is a,p,q,b

--> p=(a+q)/2 and q=(p+b)/2

--> 2p = a+q and 2p = p+b ------ (2)

To prove : G^2 =(2p-q)(2q-p)

RHS = (2p-q)(2q-p)

= (a+q-q)(p+b-p) {from (2)}

= ab

= G^2 {proved above in (1)}

= LHS

HENCE PROVED

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If one geometric mean G and two arithmetic mean A & B are inserted between two given quantities , then find (2A-B)(2B-A) a) 2G b) G C) G^2 d) G^3?

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If one geometric mean G and two arithmetic mean A & B are inserted between two given quantities , then find (2A-B)(2B-A) a) 2G b) G C) G^2 d) G^3? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If one geometric mean G and two arithmetic mean A & B are inserted between two given quantities , then find (2A-B)(2B-A) a) 2G b) G C) G^2 d) G^3? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one geometric mean G and two arithmetic mean A & B are inserted between two given quantities , then find (2A-B)(2B-A) a) 2G b) G C) G^2 d) G^3?.

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