Question

sall am si eu o problema.

1. Stiind ca x-1/x=2, calculati x²+1/x².
2. Stiind ca a-b=1, calculati a²+b²-2ab+2a-2b+1.
3. Stiind ca a+b=4 si ac+ad+bc+bd=4√3, calculati c+d.

Answer 1

2. (a-b) ^2= 1^2= 1; 2(a-b) = 2; a^2+ b^2-2ab= 1; 2a-2b = 2; rezulta 1+ 2+ 1= 4; 3. ac+ ad+ bc+ bd= c( a+ b) + d( a+ b) = ( a+b)(c+d) = 4(c+d) = 4 rad3 ; se imparte la 4 si rezulta ca c+ d = rad3; x-1/x= 1-1/x= 2; -1/x = 1; 1/x = -1; 1/x^2 = (-1)^2= 1; x^2+ 1/x^2= 1+ 1/x^2 = 1+ 1= 2