Matematică
analissanicegi
4

Rezolvati in IR ecuatia:a)[latex] \frac{3}{x-5}- \frac{x}{x+1}= \frac{10}{(x+1)(x-5)};b) \frac{16}{x-2}- \frac{6}{x}= \frac{21}{x+3};c) \frac{x^{2}+x}{x-1}+2x=\frac{3x-1}{x-1}+2 .[/latex]

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(1) Răspunsuri
yulyayo95

a) 3/(x-5)-x/(x+1)=10/(x+1)(x-5) 3(x+1)-x(x-5)=10 3x+3-x²+5x-10=0 x²-8x+7=0 Δ=(-8)²-4×7=64-28=36 x₁=(8+√64)/2=(8+6)/2=7 x₂=(8-√64)/2=(8-6)/2=1 b) 16/(x-2)-6/x=21/(x+3) (16x-6x+12)/x(x-2)=21/(x+3) (10x+12)/(x²-2x)=21/(x+3) 21x²-42x=10x²+12x+30x+36 11x²-84x-36=0 Δ=(-84)²+4×36×11=7056+1584=8640 x₁=(84+√8640)/22=(42+12√15)/11 x₂=(84-√8640)/22=(42-12√15)/11 c) (x²+x)/(x-1)+2x=(3x-1)/(x-1)+2 x²+x+2x²-2x=3x-1+2x-2 3x²-6x+3=0 x²-2x+1=0 (x-1)²=0 x-1=0 x=1

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