Toán Lớp 8: a) 2x-1/3 – 5x+2/7 = x+3
B ) (x+4)(5x+9)-x^2+16=0
c) x^3+1+(x^2-x+1)=0
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Toán Lớp 8: a) 2x-1/3 – 5x+2/7 = x+3
B ) (x+4)(5x+9)-x^2+16=0
c) x^3+1+(x^2-x+1)=0
Comments ( 2 )
Giải đáp+Lời giải và giải thích chi tiết:
a) (2x-1)/3-(5x+2)/7=x+3
<=>(7(2x-1))/21-(3(5x+2))/21=(21(x+3))/21
<=>14x-7-15x-6=21x+63
<=>21x-14x+15x=-7-6-63
<=>22x=-76
<=>x=-38/11
Vậy x=-38/11
b) (x+4)(5x+9)-x^2+16=0
<=>(x+4)(5x+9)-(x^2-16)=0
<=>(x+4)(5x+9)-(x-4)(x+4)=0
<=>(x+4)(5x+9-x+4)=0
<=>(x+4)(4x+13)=0
<=>\(\left[ \begin{array}{l}x+4=0\\4x+13=0\end{array} \right.\)
<=>\(\left[ \begin{array}{l}x=-4\\x=\dfrac{-13}{4}\end{array} \right.\)
Vậy x\in{-4; -13/4}
c) x^3+1+(x^2-x+1)=0
<=>(x+1)(x^2-x+1)+(x^2-x+1)=0
<=>(x^2-x+1)(x+1+1)=0
<=>(x^2-x+1)(x+2)=0
Ta có: x^2-x+1=(x-1/2)^2+3/4>0 với mọi x
=>x+2=0
<=>x=-2
Vậy x=-2
a. (2x-1)/3 -(5x+2)/7 = x +3
[7.(2x-1) – 3.(5x+2)]/21 = x + 3
( 14x – 7 – 15x – 6)/21 = x + 3
( -x – 13 )/21 = x + 3
-x – 13 = 21x + 63
22x = 76
x = 38/11
Vậy x = 38/11
b. (x+4).(5x + 9) – x^2 + 16 = 0
(x+4).(5x+9) – (x-4).(x+4) = 0
(x+4).(5x + 9 – x + 4) = 0
(x+4).(4x + 13) = 0
=> {{:(x + 4 = 0),(4x + 13 = 0):}
<=> {{:(x = -4),(x = -13/4):}
Vậy x in {-4;-13/4}.
c. x^3 + 1 + (x^2 – x + 1) = 0
( x + 1).(x^2 – x + 1) + ( x^2 – x + 1) = 0
(x + 1 + 1).(x^2 – x + 1 ) = 0
( x + 2 ).( x^2 – x + 1)= 0
=> {{:(x + 2 = 0),(x^2 – x + 1 = 0):}
<=> {{:(x = -2),(x^2 – x + 1/4 – ( 1/4 – 1 ) = 0 ):}
<=> {{:(x = -2),( (x – 1/2)^2 + 3/4 = 0 ):}
– Vì (x- 1/2)^2 > 0 mà khi công thêm 3/4 thì nó không thể bằng 0:
<=> {{:(x = -2),( Vô lý ):}
Vậy x = -2.