+91-87964 74404
FlagBACK
Question icon
Grade 11Algebra

Let a, b, be positive real numbers. If a, A1, A2 b are in arithmetic progression, a, G1, G2, b are in geometric progression and a, H1, H2, b are in harmonic progression,
show that G1 G=G2/H1 H2 = A1 + A2/ H1 H2 = (2a + b) (a + 2b)/ 9ab

Profile image of Simran Bhatia
12 Years agoGrade 11
Answers icon

1 Answer

Profile image of Aditi Chauhan
12 Years ago
Hello Student,
Please find the answer to your question
Clearly A1 + A2 = a + b
1/H1 + 1/H2 = 1/a + 1/b
⇒ H1 + H2/H1 H2 = a + b/ab = A1 + A2/G1 G2
⇒ G1 G2 / H1 H2 = A1 + A2/H1 + H2
Also 1/H1 = 1/a + 1/3 (1/b – 1/a) ⇒ H1 = 3ab/2b + a
1/H2 = 1/a + 2/3(1/b – 1/a) ⇒ H2 = 3ab/2a + b
⇒ A1 + A2/H1 + H2 = \frac{a+b}{3ab\left ( \frac{1}{2b+a}+\frac{1}{2a+b} \right )}
= \frac{\left ( 2b+a \right )\left ( 2a+b \right )}{9ab}

Thanks
Aditi Chauhan
askIITians Faculty

Other Related Questions on algebra

question mark
What is a binomial expression?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
Can we divide two vectors? If this is possible then how?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
How do you write “the product of 18 and q” as an algebraic expression?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
algebra
1 Answer Available

Last Activity: 3 Years ago

question mark
Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?
algebra
1 Answer Available

Last Activity: 3 Years ago