Discussion

Explanation:

Given, 41+2+3

We first multiply and divide by 1 - (√2 + √3)

41+2+3 = 41+2+3 × 1-(2+3)1-(2+3)

⇒ 41+2+3 = 41-(2+3)12-(2+3)2

⇒ 41+2+3 = 41-(2+3)1-(5+26)

⇒ 41+2+3 = 41-(2+3)-(4+26)

⇒ 41+2+3 = 2(2+3)-12+6

Now, we multiply and divide by 2 - √6

⇒ 41+2+3 = 2(2+3)-12+6 × 2-62-6

⇒ 41+2+3 = 2(2+3)-1×(2-6)22-62

⇒ 41+2+3 = 2(2+3)-1×(2-6)-2

⇒ 41+2+3 = [(√2 + √3) - 1] × (√6 - 2)

⇒ 41+2+3 =  √12 - 2√2 + √18 - 2√3 - √6 + 2

⇒ 41+2+3 =  2√3 - 2√2 + 3√2 - 2√3 - √6 + 2

⇒ 41+2+3 =  √2 - √6 + 2

Hence, option (c).

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