(2+√3)^4 + 1/(2+√3)⁴=
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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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