Toán Lớp 7: tìm x: 1, (x+1/x-1)-(x-1/x+1)=4/x^2-1 2,(x+4/x-1)+(x-1/x+1)=16/x^2-1 3,x(2x-9)=3x(x-5) 4,0,5x(x-3)=(x-3)(1,5x-1) 5,(3/7x)-1=(1/7x)(3x-7

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Toán Lớp 7:  tìm x: 1, (x+1/x-1)-(x-1/x+1)=4/x^2-1 2,(x+4/x-1)+(x-1/x+1)=16/x^2-1 3,x(2x-9)=3x(x-5) 4,0,5x(x-3)=(x-3)(1,5x-1) 5,(3/7x)-1=(1/7x)(3x-7) 6,8x(3x-5)=6(3x-7)

truongankimtrong · Answer

Giải đáp+Lời giải và giải thích chi tiết: 1) (x+1)/(x-1)-(x-1)/(x+1)=4/(x^2-1) (ĐKXĐ: x ne±1) <=> ((x+1)^2)/(x^2-1)-((x-1)^2)/(x^2-1)=4/(x^2-1) => x^2+2x+1-x^2+2x-1=4 <=> 4x =4 <=> x =1(KTM) Vậy phương trình 1) vô nghiệm 2) (x+4)/(x-1)+(x-1)/(x+1)=(16)/(x^2-1)(ĐKXĐ: x ne±1) <=> ((x+4)(x+1))/(x^2-1)+((x-1)^2)/(x^2-1)=(16)/(x^2-1) => x^2+5x+4+x^2-2x+1-16=0 <=> 2x^2+3x-11=0 <=> x^2+3/2x-(11)/2=0 <=> x^2+2. x . 3/4 +9/(16)-(97)/(16)=0 <=> (x+3/4)^2=( sqrt{97})/(16) <=> ( left[ begin{array}{l}x+ dfrac{3}{4}= dfrac{ sqrt{97}}{16} x+ dfrac{3}{4}= - dfrac{ sqrt{97}}{16} end{array} right. ) <=> ( left[ begin{array}{l}x= dfrac{ sqrt{97}}{16}- dfrac{3}{4}(t/m) x= dfrac{- sqrt{97}}{16}- dfrac{3}{4}(t/m) end{array} right. ) 3) x(2x-9)=3x(x-5) <=> 2x^2-9x = 3x^2 - 15x <=> x^2-6x=0 <=> x(x-6)=0 <=> ( left[ begin{array}{l}x=0 x-6=0 end{array} right. ) <=> ( left[ begin{array}{l}x=0 x=6 end{array} right. ) 4) 0,5x(x-3)=(x-3)(1,5x-1) <=>0,5x(x-3)-(x-3)(1,5x-1)=0 <=> 0,5x^2-1,5x-(1,5x^2-5,5x+3)=0 <=> 0,5x^2-1,5x-1,5x^2+5,5x-3=0 <=> -x^2+4x-3=0 <=> x^2-4x+3=0 <=>(x-3)(x-1)=0 <=> ( left[ begin{array}{l}x-3=0 x-1=0 end{array} right. ) <=> ( left[ begin{array}{l}x=3 x=1 end{array} right. ) 5) 3/7x-1=1/7x(3x-7) <=> 3/7x-1-1/7x(3x-7)=0 <=> 3/7x-1-3/7x^2+x=0 <=> -3/7x^2+(10)/7x-1=0 <=> (3/7x-1)(1-x)=0 <=> ( left[ begin{array}{l} dfrac{3}{7}x-1=0 1-x=0 end{array} right. ) <=> ( left[ begin{array}{l} dfrac{3}{7}x=1 x=1 end{array} right. ) <=> ( left[ begin{array}{l}x= dfrac{7}{3} x=1 end{array} right. ) 6) 8x(3x-5)=6(3x-7) <=> 8x(3x-5)-6(3x-7)=0 <=> 24x^2-40x - 18x+42=0 <=> 24x^2-58x+42=0 <=> 4x^2-(29)/3x+7=0 <=> (2x)^2-2.2x.(29)/(12)+(841)/(144)+(167)/(144)=0 <=> (2x-(29)/(12))^2=-(167)/(144)(vô nghiệm) Vậy phương trình 6) vô nghiệm

giahan44 · Answer

Đáp án:       Giải thích các bước giải: