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1 For Problems 1 through 8: Find the following polynomials Irro(a,x). Hint: Set r=a, and work to eliminate the roots. .4 1 Ir

answer number 6,7,8

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Answer #1

\\6.\\x=(\sqrt 5-1)^{\frac{1}{3}}\\ => x^3=\sqrt 5-1\\ => x^3+1=\sqrt 5\\ =>(x^3+1)^2=5\\ =>x^6+2x^3-4=0\\\\7.\\x=\sqrt {3^{\frac{1}{4}}+1}\\ =>x^2=3^{\frac{1}{4}}+1\\ =>x^2-1=3^{\frac{1}{4}}\\ =>(x^2-1)^4=3\\ =>(x^4-2x^2+1)(x^4-2x^2+1)=3\\ =>x^8-4x^6+6x^4-4x^2-2=0\\8.\\x=(\sqrt 2 -1)^{\frac{1}{4}}\\ =>x^4+1=\sqrt 2 \\ =>(x^4+1)^2=2\\ =>x^8+2x^4-1=0

answered by: ANURANJAN SARSAM
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