Rozwiąż równanie, korzystając ze wzorów skróconego mnożenia.   a) 100x^{2}  - 81 = 0 b)frac{1}{4}x^{2} - frac{1}{9} = 0 c) x^{2} + 10x + 25 = 0 d)x^{2} + 64 = 16x e) 24x -x^{2} = 144 f)x^{2} + 6x + 1 =0     zadanie potrzebuję pilnie na dzisiaj !!!

a) 100x^2 - 81 = 0 (10x - 9)*(10x + 9) = 0 10x - 9 = 0  v  10x + 9 = 0 10x = 9       v  10 x = - 9 x = 9/10     v       x = - 9/10 ============================ b) (1/4) x^2 - 1/9 = 0 [ (1/2) x - 1/3)*((1/2)x + 1/3) = 0 (1/2)x - 1/3 = 0   v  (1/2) x + 1/3 = 0 (1/2)x = 1/3        v   (1/2) x = - 1/3   / * 2 x = 2/3                v            x = - 2/3 ===================================== c) x^2 + 10 x + 25 = 0 (x + 5)^2 = 0 x + 5 = 0 x = - 5   - pierwiastek podwójny ======= d) x^2 + 64 = 16x x^2 - 16x + 64 = 0 (x - 8)^2 = 0 x - 8 = 0 x = 8  - pierwiastek podwójny ========================= e) 24 x - x^2 = 144 x^2 - 24x + 144 = 0 ( x - 12)^2 = 0 x - 12 = 0 x = 12  - pierwiastek podwójny ============================== f) x^2 + 6x + 1 = 0 delta = 6^2 - 4*1*1 = 36 - 4 = 32 = 16*3 p(delty) = 4 p(3) x1 = [ - 6 - 4 p(3)]/2 = - 3 - 2 p(3) x2 = [ - 6 + 4 p(3)]/2 = - 3 + 2 p(3) ================================ p(3)  - pierwiastek kwadratowy z 3