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a. 9x−0,74−5x−1,57=7x−1,13−5(0,4−2x)69x−0,74−5x−1,57=7x−1,13−5(0,4−2x)6
⇔21(9x−0,7)84−12(5x−1,5)84⇔21(9x−0,7)84−12(5x−1,5)84 = 28(7x−1,1)84−70(0,4−2x)8428(7x−1,1)84−70(0,4−2x)84
⇔21(9x−0,7)−12(5x−1,5)=28(7x−1,1)−70(0,4−2x)⇔189x−14,7−60x+18=196x−30,8−28+140x⇔189x−60x−196x−140x=−30,8−28+14,7−18⇔−207x=−62,1⇔x=0,3⇔21(9x−0,7)−12(5x−1,5)=28(7x−1,1)−70(0,4−2x)⇔189x−14,7−60x+18=196x−30,8−28+140x⇔189x−60x−196x−140x=−30,8−28+14,7−18⇔−207x=−62,1⇔x=0,3
Vậy phương trình có nghiệm x = 0,3
b. 3x−1x−1−2x+5x+3=1−4(x−1)(x+3)3x−1x−1−2x+5x+3=1−4(x−1)(x+3) ĐKXĐ: x≠1x≠1và x≠3x≠3
⇔(3x−1)(x+3)(x−1)(x+3)−(2x+5)(x−1)(x−1)(x+3)=(x−1)(x+3)(x−1)(x+3)−4(x−1)(x+3)⇔(3x−1)(x+3)−(2x+5)(x−1)=(x−1)(x+3)−4⇔3x2+9x−x−3−2x2+2x−5x+5=x2+3x−x−3−4⇔3x2−2x2−x2+9x−x+2x−5x−3x+x=−3−4+3−5⇔3x=−9⇔(3x−1)(x+3)(x−1)(x+3)−(2x+5)(x−1)(x−1)(x+3)=(x−1)(x+3)(x−1)(x+3)−4(x−1)(x+3)⇔(3x−1)(x+3)−(2x+5)(x−1)=(x−1)(x+3)−4⇔3x2+9x−x−3−2x2+2x−5x+5=x2+3x−x−3−4⇔3x2−2x2−x2+9x−x+2x−5x−3x+x=−3−4+3−5⇔3x=−9
⇔x=−3⇔x=−3 (loại)
Vậy phương trình vô nghiệm
c. 34(x−5)+1550−2x2=−76(x+5)34(x−5)+1550−2x2=−76(x+5) ĐKXĐ: x≠±5x≠±5
⇔34(x−5)+152(25−x2)=−76(x+5)⇔34(x−5)−152(x+5)(x−5)=−76(x+5)⇔9(x+5)12(x+5)(x−5)−9012(x+5)(x−5)=−14(x−5)12(x+5)(x−5)⇔9(x+5)−90=−14(x−5)⇔9x+45−90=−14x+70⇔9x+14x=70−45+90⇔23x=115⇔34(x−5)+152(25−x2)=−76(x+5)⇔34(x−5)−152(x+5)(x−5)=−76(x+5)⇔9(x+5)12(x+5)(x−5)−9012(x+5)(x−5)=−14(x−5)12(x+5)(x−5)⇔9(x+5)−90=−14(x−5)⇔9x+45−90=−14x+70⇔9x+14x=70−45+90⇔23x=115
⇔x=5⇔x=5 (loại)
Vậy phương trìnhvô nghiệm
d. 8x23(1−4x2)=2x6x−3−1+8x4+8x8x23(1−4x2)=2x6x−3−1+8x4+8x ĐKXĐ: x≠±12x≠±12
⇔8x23(1−2x)(1+2x)=−2x3(1−2x)−1+8x4(1+2x)⇔32x212(1−2x)(1+2x)=−8x(1+2x)12(1−2x)(1+2x)−3(1+8x)(1−2x)12(1−2x)(1+2x)⇔32x2=−8x−16x2−3(1−2x+8x−16x2)⇔32x2=−8x−16x2−3−18x+48x2⇔32x2+16x2−48x2+18x+8x=−3⇔26x=−3⇔8x23(1−2x)(1+2x)=−2x3(1−2x)−1+8x4(1+2x)⇔32x212(1−2x)(1+2x)=−8x(1+2x)12(1−2x)(1+2x)−3(1+8x)(1−2x)12(1−2x)(1+2x)⇔32x2=−8x−16x2−3(1−2x+8x−16x2)⇔32x2=−8x−16x2−3−18x+48x2⇔32x2+16x2−48x2+18x+8x=−3⇔26x=−3
⇔x=−326⇔x=−326 (thỏa mãn)
Vậy phương trình có nghiệm x=−326
Ta có
5(3x + 5) − 4(2x − 3) = 5x + 3(2x − 12) + 1
ó 15x + 25 − 8x + 12 = 5x + 6x – 36 + 1
ó 7x + 37 = 11x − 35
ó 4x = 72
ó x = 18
Vậy x = 18.
Suy ra 17 < x < 19.
Đáp án cần chọn là: C