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The a.p between a and b is twice the g.p between a and b . Prove that a/b = 7+4root 3 or 7- 4root3. Plzz answer this

The a.p between a and b is twice the g.p between a and b . Prove that a/b = 7+4root 3 or 7- 4root3. Plzz answer this

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear Vaibhav
 
Let A be the arithmetical mean and G be the geometrical mean between a and b .
So .. A = 2G given
Therefore (a+b)÷2 = 2 (under root of ab)
a+b= 4 (Sq rt ab) ..
(a+b)/ (Sq rt ab) = 4
We can write it
(a/ Sq root of ab) + (b/Sq root of ab) =4
It means 
Sq root of (a/b) + Sq root of b/a) = 4
Let a/b = ' k ' say in above equation (because we have to define a:b means a/b)
Sq root of k + sq root of (1/k) =4
Squaring both sides we get
k +(1/k)+2 =16
Multiply both sides by k we get after solving 
k^2 -14 k +1 = 0
Solve for k we get
k = 7+4 (Sq root of 3) or
k= 7 - 4 (Sq root of 3)
 
 
Regards
Arun (askIITians forum expert)

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