pt <=> x4-2x2+1+4x2-8x+4=12x2+24x+12
<=> x4=10x2+32x+7
<=> x4+6x2+9=16x2+32x+16
<=> (x2+3)2=16(x+1)2
<=> x2+3=4(x+1) (1) hoac x2+3=-4(x+1) (2)
(1) <=> x2-4x-1=0 <=> \(x=2+\sqrt{5}\)hoac \(x=2-\sqrt{5}\)
(2) <=> x2+4x+7=0 pt vo nghiem
Vay: pt co nghiem \(x=2+\sqrt{5}\)hoac \(x=2-\sqrt{5}\)
1)Giai phuong trinh:
a) x4+4x2-5=0
b)Cho phuong trinh: x2-2(m+1)x+m2+3m-4=0(1)
Giai phuong trinh khi m=2Chung minh phuong trinh luon co nghiem voi moi m.Goi x1,x2 la nghiem cua phuong trinh,tim m de thoa man dieu kien:x12+x22=10giai phuong trinh
\(\left(2x-1\right)^2=12\sqrt{x^2-x-2}-1\)
giai phuong trinh :(1+x)^8 + (1+x^2)^4 = 2x^4
giai he phuong trinh
x+2\x+1\y=4
1\x^2+1\xy+x\y=3
Cho phuong trinh bac hai 4x^2-2(√10)+1=0 co hai nghiem x1,x2.Khong giai phuong trinh, hay tinh gia tri bieu thuc(√x14+8x22)+(√x24+8x12).
\(\frac{x^2-8}{x^2-16}=\frac{1}{x+4}+\frac{1}{x-4}\)
giai phuong trinh
x^2+(x^2/(x+1)^2)=1
giai phuong trinh
Cho phuong trinh : x2 +( 2m-1 )x +2(m-1) = 0
a) Giai phuong trinh khi m= 2
b) Chung minh phuong trinh co nghiem voi moi m
c) Tim m de phuong trinh co 2 nghiem x1 , x2 thoa man x1 ( x2 - 5 ) + x2 ( x1 - 5 ) = 33
a) Cho phuong trinh x2 +mx+1=0. Tim dieu kien cua m de phuong trinh co nghiem kep. Tinh nghiem kep do
b) Khong giai phuong trinh, chung to phuong trinh 2x2 - 3x - 5 = 0co 2 nghiem phan biet x1 , x2. Tinh ( x1 - x2 )
