Question

[Lý Khánh Linh]

Cho x>y>0 và x-y=7; x.y= 60

Tính :a) x^2-y^2                        b) x^4+y^4

Answer 1

[Nguyễn Thị BÍch Hậu]

a) \(x^2-y^2=\left(x-y\right)\left(x+y\right)=7.\left(x+y\right)\)

ta có: \(\left(x-y\right)^2=49\Leftrightarrow x^2+y^2-2xy=49\Leftrightarrow\left(x^2+y^2+2xy\right)-4xy=49\Leftrightarrow\left(x+y\right)^2=289\Leftrightarrow x+y=17\)

=> A= 7.17=119

b) \(x^4+y^4=\left(x+y\right)^4-\left(4x^3y+6x^2y^2+4xy^3\right)=17^4-2xy\left(2x^2+3xy+2y^2\right)=17^4-120\left[2\left(x^2+y^2\right)+3.60\right]\)

\(=17^4-120\left[2\left(x^2+y^2\right)+3.60\right]==17^4-120\left[2.119+3.60\right]=33361\)

Answer 2

[Ác Mộng]

Từ x-y=7 xy=60=>(x-y)²+2xy=7²+2.60=>x²+y²=169

=>(x-y)²+4xy=7²+4.60

=>x²-2xy+y²+4xy=49+240

=>(x+y)²=289

=>x+y=17 hoặc x+y=-17

a)x²-y²=(x-y)(x+y)=7(x+y)

*)x+y=17=>x²-y²=7.17=119

*)x+y=-17=>x²-y²=7.(-17)=-119

b)Ta có:(x+y)⁴=17⁴=(-17)⁴=83521

=>x⁴+y⁴+4x³y+4xy³+6x²y²=83521

=>x⁴+y⁴+4xy(x²+y²)+6.(60²)=83521

=>x⁴+y⁴+4.60.169+21600=83521

=>x⁴+y⁴+62160=83521

=>x⁴+y⁴=21361