Question

a,b,c is a geometric progression (a,b,c are real numbers ). If a+b+c=26 and a^2+b^2+c^2=364. Find b.

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

b = 6

Step-by-step explanation:

Given data

a, b, c are in geometric progression and real numbers

a+b+c = 26 and a² + b² + c² = 364  

here we need to find value of b

⇒ from given data a, b, c are Geometric progression

⇒ $\frac{b}{a} = \frac{c}{b}$ ⇒  b² = ca _ (1)

⇒ from algebraic identities we know that

    (a+b+c)² = a² +b² +c² + 2 ab + 2 bc + 2 ca  

     ⇒ (26)²  =  364 + 2(ab + bc + ca)

     ⇒  676 - 364 = 2 ( ab + bc + ca )

     ⇒ 2 (ab + bc + ca) = 312

     ⇒  ab + bc + b² = 312/2    [ from (1) ]

     ⇒  b ( a + b + c ) = 156     [ take b common ]

     ⇒  b (26) =  156    [ from given data]

     ⇒  b = 156/ 26 = 6

⇒ the value of b = 6