Question

(2+√3)^4 + 1/(2+√3)⁴=​

Answer 1

Answer:

Exact form : 98 - 56√3

Decimal form : 1.00515477...

Step-by-step explanation:

(2 +√3)^4 + 1/(2 +√3)⁴

Simplify the numerator

98 + 56√3/(2 +√3)⁴

Using Binomial theorem

98 + 56√3/2^4 + 4 × 2^3 + 6 × 2^2√3^2 + 4 × 2√3^3 + √3^4

Simplify terms

98 + 56√3/97 + 56√3

Multiply 98 + 56√3/97 + 56√3 by 97 - 56√3/97 - 56√3

98 + 56√3/97 + 56√3 × 97 - 56√3/97 - 56√3

Combine fractions

(98 + 56√3) (97 - 56√3)

Expand (98 + 56√3) (97 - 56√3) using the FOIL method

98 × 97 + 98 (-56√3) + 56√3 × 97 + 56√3(-56√3)

Simplify and combine like terms

98 - 56√3

The result can be shown in multiple forms :

Exact form : 98 - 56√3

Decimal form : 1.00515477...

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