ICSE Class 10CISCE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

If a = (4sqrt6)/(Sqrt2 + Sqrt3) Find the Value of (A + 2sqrt2)/(A - 2sqrt2) + (A + 2sqrt3)/(A - 2sqrt3) - ICSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

If a = `(4sqrt6)/(sqrt2 + sqrt3)` find the value of `(a + 2sqrt2)/(a - 2sqrt2) + (a + 2sqrt3)/(a - 2sqrt3)`

Solution

a = `(4sqrt6)/(sqrt2 + sqrt3)`

`a/(2sqrt2) = (2sqrt3)/(sqrt2 + sqrt3)`

Applying componendo and divendo

`(a + 2sqrt2)/(a - 2sqrt2) = (2sqrt3 + sqrt2 + sqrt3)/(2sqrt3 - sqrt2 - sqrt3)`

`(a + 2sqrt2)/(a - 2sqrt2) = (3sqrt3 + sqrt2)/(sqrt3 - sqrt2)`  ....(1)

`a/(2sqrt3) = (2sqrt2)/(sqrt2 + sqrt3)`

Applying componendo and dividendo

`(a + 2sqrt3)/(a - 2sqrt3) = (2sqrt2 + sqrt2 + sqrt3)/(2sqrt2 - sqrt2 - sqrt3)`

`(a + 2sqrt3)/(a - 2sqrt3) = (3sqrt2 + sqrt3)/(sqrt2 - sqrt3)`  ...(2)

From (1) and (2)

`(a + 2sqrt2)/(a - 2sqrt2) + (a + 2sqrt3)/(a - 2sqrt3) = (3sqrt3 + sqrt2)/(sqrt3 - sqrt2) + (3sqrt2 + sqrt3)/(sqrt2 - sqrt3)`

`(a + 2sqrt2)/(a - 2sqrt2) + (a + 2sqrt3)/(a - 2sqrt3) = (3sqrt2 + sqrt3 - 3sqrt3 - sqrt2)/(sqrt2 - sqrt3)`

`(a + 2sqrt2)/(a - 2sqrt2) +(a + 2sqrt3)/(a - 2sqrt3) = (2sqrt2 - 2sqrt3)/(sqrt2 - sqrt3)  = 2`

  Is there an error in this question or solution?

APPEARS IN

 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7C | Q: 6.2

Video TutorialsVIEW ALL [1]

Solution If a = (4sqrt6)/(Sqrt2 + Sqrt3) Find the Value of (A + 2sqrt2)/(A - 2sqrt2) + (A + 2sqrt3)/(A - 2sqrt3) Concept: Componendo and Dividendo Properties.
S
View in app×