Zad1 Rozwiąż równanie: a)√2x-1 / √2x+1 =√2x+1 b)3/x+2 = 1/x-2 c) 1/x + x/x+2 =1 d) 1/x-1 + 1/x+2= 3/(x-1)(x+2)

a)√2x-1 / √2x+1 =√2x+1 (1+√2x)(1-√2x) = √2x+1 1-4x=√2x+1 -4x=√2x (-4x) 2 = 2x 16x = 2x 14x=0 x=0 b)3/x+2 = 1/x-2 / *(x-2) 3/x+2 *x-2 =1 3x-6/x(kwadrat)-4 = 1 /*x(kwadrat)-4 3x-6=3/x(kwadrat)-4 3x=x(kwadrat)+2 x=x(kwadrat)+2/3 c) 1/x + x/x+2 =1 / (x+2) x+2/x(kwadrat)+2+x=x+2 x+2/x(kwadrat)+2=2 /:x(kwadrat)+2 x+2=x(kwadrat)+4 x=x+(kwadrat)+2 d) 1/x-1 + 1/x+2= 3/(x-1)(x+2) /*(x+2) 1/0,5+1=3/0,5 równanie sprzeczne

a)√2x-1 / √2x+1 =√2x+1 b)3/x+2 = 1/x-2 c) 1/x + x/x+2 =1 d) 1/x-1 + 1/x+2= 3/(x-1)(x+2) a)√2x-1-√2x+1=√2x+1 /*(√2x+1) √2x-1= (√2x+1)(√2x+1) √2x-1= 2x²+√2x+√2x+1 √2x-1= 2x²+2√2+1 √2x-2√2x-1-1-2x²=0 2x²-√2x-2=0 Δ=b²-4ac Δ= 2+16 Δ= 18 √Δ= 3√2 x₁= -b-√Δ/2a x₁= √2-3√2/4= √2/2 x₂= -b+√Δ/2a x₂= √2+3√2/4=4√2/4=√2 x∈ (√2/2,√2) b)3/x+2 = 1/x-2 3/x-1/x=-2-2 2/x=-4 /*x 2=-4x x=-1/2 c)1/x + x/x+2 =1 /x 1+x+2x=x 1=-3x x=-1/3 d)1/x-1 + 1/x+2= 3/(x-1)(x+2) 1(x+2)/(x-1)(x+2) + 1(x-1)/(x-1)(x+2)= 3/(x-1)(x+2) x+2/(x-1)x+2)+ x-1/(x-1)(x+2)= 3/(x-1)(x+2) 2x-1/(x-1)(x+2) - 3/(x-1)(x+2)=0 2x-4/(x-1)(x+2)=0 /*(x-1)(x+2) 2x-4=0 2x=4 x=2