Question

three positive no.s a,b,c are in G.p prove that a+c greater than 2b​

Answer 1

Answer:

Answer:

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Step-by-step explanation:

Step-by-step explanation:

Answer 2

Answer:

a + c > 2b

Step-by-step explanation:

Three unequal positive numbers a, b, c are in gp

let say three numbers are

a , ar , ar²

a = a

b = ar

c = ar²

to be proved that

a + c > 2b

a + c > 2b

iff a + ar² > 2ar

iff a + ar² - 2ar > 0

iff a(1 + r² - 2r) > 0

iff a(1 - r)² > 0

a is a +ve number & square is always +ve

=> a(1 - r)² > 0 if r≠1 and r can not be = 1 as a , b , c are unequal number

Hence Proved

a + c > 2b