1. ((X+3) / (x-3)) + ((x-3) / (x+3)) = 10/3 2. ((X+1) / (x-1)) + ((x-1) / (x+1)) = 2.1/2

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18 января, 02:30

1. ((X+3) / (x-3)) + ((x-3) / (x+3)) = 10/3 2. ((X+1) / (x-1)) + ((x-1) / (x+1)) = 2.1/2

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1. х+3/х-3=t ⇒t+1/t=10/3⇒t^2+1=10/3*t

3t^2-10t+3=0 D=100-36=64 √64=8

t1=1/6 * (10+8) = 3 t2=1/6 * (10-8) = 1/3

t=3 x+3/x-3=3 x+3=3x-9 2x=12 x=6

t=1/3 x+3=1/3*x-1 2/3x=-4 x=-4*3/2=-6

2. x+1/x-1=t t+1/t=5/2 t^2-5/2·t+1=0⇒2t^2-5t+2=0

D=25-4*2*2=9 √9=3

t1=1/4 * (5+3) = 2 t2=1/4 * (5-3) = 1/2

t=2 x+1/x-1=2 x+1=2x-2 x=3

t=1/2 x+1=0.5x-0.5 0.5x=-3/2 x=-3