Rozwiąż rówanie; 4(x+2)^2 - 2(x-1)^2 = -8   Rozwiąż nierówność:   4(x-3)^2 - (2x-5)^2 >(większe bądź równe) 2

1. 4(x+2)^2 - 2(x-1)^2 = -8 4(x^2+2*2*x+2^2) - 2(x^2-2*x*1+1^2) = -8 4(x^2+4x+4) - 2(x^2-2x+1) = -8 4x^2 + 16x + 16 - 2x^2 + 4x - 2 = -8 2x^2 + 20x + 14 = -8 /+8 2x^2 + 20x + 22 = 0 /:2 x^2 + 10x + 11 = 0 delta = b^2 - 4a*c = 10^2 - 4*1*11 = 100 - 44 = 56 [latex] sqrt{delta} [/latex] = [latex] sqrt{56} = 2 sqrt{14} [/latex] [latex] x_{1} = frac{-b- sqrt{delta}}{2*a} = frac{-10-2 sqrt{14}}{2*1} = frac{-2(5+ sqrt{14})}{2} = -(5 + sqrt{14} )[/latex] [latex] x_{2} = frac{-b+ sqrt{delta}}{2*a} = frac{-10+2 sqrt{14}}{2*1} = frac{-2(5- sqrt{14})}{2} = -(5-sqrt{14})[/latex] 2. 4(x-3)^2 - (2x-5)^2 [latex] geq [/latex] 2 4(x^2-3*2*x+3^2) - ((2x)^2 - 5*2*2x + 5^2) [latex] geq [/latex] 2 4(x^2-6x+9) - (4x^2-20x+25) [latex] geq [/latex] 2 4x^2 - 24x + 36 - 4x^2 + 20x - 25 [latex] geq [/latex] 2 - 4x + 11 [latex] geq [/latex] 2 /-11 - 4x [latex] geq [/latex] 2 - 11 - 4x [latex] geq [/latex] -9 /:(-4) x [latex] leq [/latex] 9/4 x [latex] leq [/latex] 2 1/4 x należy do (-nieskończoność, 2 1/4 >