Question

Oblicz wartość liczbową wyrażeń

(ax+1)²-(ax+1)(ax-1)+ax+1 dla a= 1/3; x=√2

(x-2)²-(3x+2)²+2(2x+1)² dla x=-1/4

Answer 1

a)(ax+1)²-(ax+1)(ax-1)+ax+1= a2x2+2ax+1-(a2x2-1)+ax+1 = a2x2+2ax+1-a2x2+1+ax+1 = 3ax+3

dla a= 1/3; x=√2

3ax+3= 3 * 1/3  *√2+3 = √2 +3

 

b) (x-2)²-(3x+2)²+2(2x+1)² = x2-4x+4-(9x2+12x+4)+2(4x2+4x+1) = x2-4x+4-9x2-12x-4+8x2+8x+2= -8x+2

dla x=-1/4

-8x+2 = -8 * (-1/4) + 2 = 2+2 = 4