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

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#### 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

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#### APPEARS IN

Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Exercise 7(C) | Q: 6.2 | Page no. 101

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