Question

if x=2+√3 then x²+1/x² simplify

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Answer 1

Answer:

Your question is solved

Answer 2

Solution:

Given , x = 2 + √3

We need to find , x² + (1/x²)

x² + 1/x²

Substituting the value of x

→ (2 + √3)² + [1/(2 + √3)²]

Using

• (a + b)² = a² + b² + 2ab

→ 2² + (√3)² + 2(2)(√3) + [1/(2² + (√3)² + 2(2)(√3)]

→ 4 + 3 + 4√3 + [1/(4 + 3 + 4√3)]

→ 7 + 4√3 + [ 1/7 + 4√3 ]

→ { [ 7 + 4√3 ]² + 1 }/{ 7 + 4√3 }

Using , the same formula

→ { 7² + (4√3)² + 2(7)(4√3) + 1 }/{ 7 + 4√3 }

→ [ 49 + 16(3) + 56√3 + 1 ]/( 7 + 4√3 )

→ [ 49 + 49 + 56√3 ]/( 7 + 4√3 )

→ ( 98 + 56√3 )/( 7 + 4√3 )

Taking common

→ 14( 7 + 4√3 )/( 7 + 4√3 )

→ 14

Hence , x² + 1/x² = 14