Question

Daca x=3√5,calculeaza :
b) (x²+x+1)²-(x²+1)(x²-1)-9(x+3)(x-3)=

c) (x²+x)-(x²-x+2)²-(2x-1)²=

d) (x√3+1)²-(x-1)²-(x+2√3)(2x-1)=

e) 3(x+1)²-(x√2-3)²-(x+6)(x+3√2)=

Va rooog.... de preferat inlocuim pe x la sfarsit

Answer 1

b) (x²+x+1)²-x⁴+1-9x²+81=
=x⁴+x³+x²+x³+x²+x+x²+x+1-x⁴+1-9x²+81=
=2x³-6x²+2x+83=2(3√5)³-6(3√5)²+2(3√5)+83=270√5-270+6√5+83=276√5-187

c) (x²+x)-(x²-x+2)²-(2x-1)²=
= x²+x-(x⁴-x³+2x²+x³-x²+2x²-2x+4)-(4x²-4x+1)=
= x²+x-x⁴+x³-2x²-x³+x²-2x²+2x-4-4x²+4x-1=
= -x⁴ -6x² +7x-5=(3√5)⁴-6(3√5)²+7(3√5)-5=2025-270+21√5-5=1750+213√5

d) (x√3+1)²-(x-1)²-(x+2√3)(2x-1)=
=3x+2x√3+1-x²+2x-1-2x²-4x√3+x+2√3=
=-3x² +6x-2x√3+2√3=
=-3(3√5)² +6(3√5)-2(3√5)√3+2√3=
=-135² +18√5-6√15+2√3

e) 3(x+1)²-(x√2-3)²-(x+6)(x+3√2)=
= 3x²+6x+3-2x+6x√2-9-x²-6x-3x√2-18√2=
= 2x²-2x+3x√2-18√2-6=
= 2(3√5)²-2(3√5)+3(3√5)√2-18√2-6=
= 90-6√5+9√10-18√2-6