Question

x=5-2√6,find the value of √x+1/√x

Answer 1

Given,

√5-2√6+1/√5-2√6

Calculation,

= √5-2√6+1/√5-2√6

= √5-2√6+1/√2+3-2√2×3

= √5-2√6+1/√2-2√2√3+3

Using a²-2ab+b²=(a-b)²,

= √5-2√6+1/√(√2-√3)²

= √5-2√6+1/√3-√2

Rationalizing the factors

= √5-2√6+1×(√3+√2)/(√3-√2)×(√3-√2)

Using (a-b)×(a+b)=a²-b²

= √5-2√6+1×(√3+√2)/3-2

= √5-2√6+1×(√3+√2)

Using a=n^√a^m

= √5-2√6+1×√(√3+√2)²

= √(5-2√6+1)×(√3+√2)

Using (a+b)²=a²+2ab+b²

= √(6-2√6)×(3+2√6+2)

= √(6-2√6)×(5+2√6)

= √30+12√6-10√6-24

= √6+2√6

Note :- the first root(√)of the equation is whole root(√).

Answer=>√6+2√6 means whole root(√)six(6) plus(+) root(√) six(6).

Hope it helps
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