Question

已知(x-y)^2=8,xy=2,求(x+y)^2,x^4+x^4的值

2. 已知x+y=4,x^2+y^2=10,求x^4+y^4的值
3. 已知x+1/x=4,求①x^2+1/x^2;②(x-1/x)^2

快一点啊哈~~

Answer 1

1.
x^4+y^4=x^4-2(xy)²+y^4+2(xy)²
=(x²-y²)²+2(xy)²
=(x-y)²(x+y)²+2(xy)²
=(x-y)²[(x-y)²+4xy]+2(xy)²
=8*[8+4*2]+2*4
=136
2.x^4+y^4=(x^2+y^2)^2-2（xy）^2
x^2+y^2=(x+y)^2-2xy
可解得：xy=3
x^4+y^4=82
3. x^2+1/x^2=(x+1/x)^2-2=14
;②(x-1/x)^2=(x+1/x)^2-4=12

Answer 2

1.(x+y)^2=（x-y）^2+4xy=8+8=16
x^4+y^4=(x^2+y^2)^2-2(x^2)(y^2)=((x-y)^2+2xy)^2-2((xy)^2)=136
2.2xy=(x+y)^2-(x^2+y^2)=6
xy=3
x^4+y^4=(x^2+y^2)^2-2(x^2)(y^2)=(x^2+y^2)^2-2((xy)^2)=82
3.x^2+1/x^2=(x+1/x)^2-2=14
(x-1/x)^2=(x^2+1/x^2)-2=12

Answer 3

1、由于（x+y）^2=(x-y)^2+4xy=8+4*2=16 (x-y)^2=x^2+y^2-2xy 故x^2+y^2=(x-y)^2+2xy=12
x^4+y^4=x^4+y^4+2x^2y^2-2x^2y^2=(x^2+y^2)^2-2x^2y^2=144-2*4=136
2、（x+y）^2=x^2+y^2+2xy 得xy=3
x^4+y^4=x^4+y^4+2x^2y^2-2x^2y^2=(x^2+y^2)^2-2x^2y^2=100-2*9=82
3、x^2+1/x^2=(x+1/x)^2-2=14
(x-1/x)^2=(x+1/x)^2-4=16-4=12
完毕

Answer 4

先简化问题x(x
y)(x-y)-x(x
y)²=x（x²-y²-x²-2xy-y²）=x（-2xy-2y²）=-2xy（x
y）
再代进数字，答案就出来了。应该是-60。