Question

已知:x=√(4-√3),y=√(4+√3),求x^6+y^6的值

Answer 1

解：∵x=√（4-√3），y=√(4+√3)
∴x^2=4-√3，y^2=4+√3，xy=√13；
x^2+y^2=8，x^2-y^2=-2√3；
又∵x^6+y^6=(x^2)^3+(y^2)^3
=(x^2+y^2)[(x^2)^2-(xy)^2+(y^2)^2]
=(x^2+y^2)[(x^2-y^2)^2+(xy)^2]
∴x^6+y^6=8*[(-2√3)^2+(√13)^2]
=8*(12+13）
=200

Answer 2

x^6+y^6
=（x²）³+（y²）³
=（4-√3）³+（4+√3）³
=（4-√3+4+√3）【（4+√3）²-（4+√3）（4-√3）+（4-√3）²】
=8×【16+3+8√3-16+3+16+3-8√3】
=8×25
=200

Answer 3

已知:x=√(4-√3),y=√(4+√3),求x^6+y^6的值
x=√(4-√3),
x^2=[√(4-√3)]^2=4-√3
,y=√(4+√3),
y^2=[√(4+√3),]^2=4+√3
x^6+y^6
=(x^2+y^2)(x^4-x^2y^2+y^4)
=(x^2+y^2)(x^4-2x^2y^2+y^4+x^2y^2)
=(x^2+y^2)[(x^2-y^2)^2+x^2y^2]
=(4-√3 + 4+√3 ) { [ 4-√3 - ( 4+√3 ) ]^2+ (4-√3 )(4+√3)}
=8*[(-2√3)^2+(16-3)]
=8*(12+13)
=200

Answer 4

104