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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`
one year ago

```							Dear Vaibhav Let A be the arithmetical mean and G be the geometrical mean between a and b .So .. A = 2G givenTherefore (a+b)÷2 = 2 (under root of ab)a+b= 4 (Sq rt ab) ..(a+b)/ (Sq rt ab) = 4We can write it(a/ Sq root of ab) + (b/Sq root of ab) =4It means Sq root of (a/b) + Sq root of b/a) = 4Let 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) =4Squaring both sides we getk +(1/k)+2 =16Multiply both sides by k we get after solving k^2 -14 k +1 = 0Solve for k we getk = 7+4 (Sq root of 3) ork= 7 - 4 (Sq root of 3)  RegardsArun (askIITians forum expert)
```
one year ago
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