Question

VA ROGG SA MA AJUTATI !!!!
E(x)=(x+5)^2+2(x+5)(x-4)+(x-4)^2,cu x€R
a)Aratati ca E(x)=(2x+1)^2 ,oricare ar fi x€R
b)Calculati E(rad2)*E(-rad2)
c)Calculati numarul real "a" pentru care E(a) are cea mai mica valoare posibila

Answer 1

a)E(x)=x²+10x+25+2(x²-4x+5x-20)+x²-8x+16
E(x)=x²+10x+25+2(x²+x-20)+x²-8x+16
E(x)=x²+10x+25+2x²+2x-40+x²-8x+16
E(x)=4x²+4x+1-descompunem
E(x)=(2x+1)²
b)E(√2)×E(-√2)=(9+4√2)×(9+4√2)=81+16×2=81+32=113
E(√2)=4×(√2)²+4×√2+1=4×2+4√2+1
E(√2)=8+4√2+1
E(√2)=9+4√2
E(-√2)=4×(-√2)²+4×(-√2)+1=4×2-4√2+1=8-4√2+1=9+4√2