Problem

Insert two numbers between 3 and 81 so that the r…

02:05

Problem 25 Easy Difficulty

If $a, b, c$ and $d$ are in G.P. show that $\left(a^{2}+b^{2}+c^{2}\right)\left(b^{2}+c^{2}+d^{2}\right)=(a b+b c+c d)^{2}$.

Answer

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Precalculus

NCERT Class 11 - Math

Chapter 9

Sequences and Series

Section 3

Series

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Video Transcript

Hello. We have problem number 25 in which it is given that if a B c D R N G P A B C D R N G P. So we have to show that, esquire plus B squared plus C squared in to be square plus the square plus the square equal to a B plus B C Felicity, whole square. So if A B C and D r n G r n A P or sorry, G P. So we should be writing it as B by a equal to see by B equal to D by C equal to our which is equal to the combined ratio. So B will be equal to they are she will be equal to B. R. If you take these two and B has value air so it will become A are square. Similarly they will be equal to see her so see so it will become a RQ. So basically we have D. Which is equal to our cue. C A R square, B A R. So let us plug in in left hand side. L. At S A squared plus B squared plus C square. So a square will be as it is A plus B square men's square are square, which is square plus see a square a square artist report for and to be a squared plus B squared plus b squared. So be square is is square. A square. Let's see. A square men's square artist apart for is quite artist about six. So let us take a square comin from this and a square comin from this. So we'll be having is squared. One place. Our square place are eligible for an A logistic is square. Our square comin from this. So it will be a square one. Place our square place. RST power to 34. For now this is a square. A square eight is too powerful. Our square. This will be one place. Our square place averaged about four whole square. So this is our left hand side now right and said it. A people is busy. A B plus busy, which means we have a B. There is a square are a squirrel plus B. C. Bc means expiring cube. Bless city. City means is where our five raised to the power took. So let us take. A square has come, esquire. Are as common. It will be a square uh squared. And here we will be having one place R squared. Place R rated R four whole square. So this is equal to our left hand side, so left hand side became equal to right and side support.

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