Question

if g1 and g2 are two geometric means between two positive number a and b then show that g1 and g2 is equals to ab​

Answer 1

Answer:

If G1 and G2 are 2 geometric means between a and b show that: (a) G1G2 = ab (b) (G1^2/ G2) + ( G2^2/G1) = a + b. a) multiply G1 and G2 we will get a2r3. on multiplying a and b the same result is obtained. hence proved.Nov 30, 2016

Step-by-step explanation:

please mark as brain list

Answer 2

Answer:

Let a, G1, G2, b are in G.P, then

G1 = √(aG2) ....(i)

Similarly G2 = √(G1b) ....(ii)

Multiplying equation (i) and (ii)

G1G2=$\sqrt{aG_{2} }$ X$\sqrt{bG_{1} }$

$\sqrt{G_{1}G_{2} } =\sqrt{ab}$

hence ${G_{1}G_{2} } ={ab}$