Question

if a,8,b are in A.P; a,4,b are in G.P; a,x,b are in H.P. then x=

Answer 1

Answer:

The value of x is 16

Step-by-step explanation:

Concept:

If a, A, b are in A.P, then $A=\frac{a+b}{2}$

If a, A, b are in G.P, then $G=\sqrt{ab}$

If a, H, b are in H.P, then $H=\frac{2ab}{a+b}$

Given:

a, 8, b are in A.P

Then,

$8=\frac{a+b}{2}$

a+b=16.........(1)

a, 4, b are in G.P

Then,

$4=\sqrt{ab}$

16=ab...........(2)

a, x, b are in H.P

Then,

$x=\frac{2(ab)}{a+b}\\\\x=\frac{2(16)}{16}\\\\x=2$

Answer 2

Answer:

x = 2

Step-by-step explanation:

if a,8,b are in A.P; a,4,b are in G.P; a,x,b are in H.P. then x=

a , 8 , b are in AP

so 8-a = b -8

=> a +b = 16   - eq1

a,4,b are in GP

4/a = b/4

=>ab = 16

a , x & b are in HP

1/x - 1/a = 1/b - 1/x

=> 2/x = 1/a + 1/b

=> 2/x = (b+a)/ab

=> x = 2ab/(a+b)

=> x = 2 * 16 / 16

=> x = 2

So value of x = 2