Question

Exercițiul 14
Va rog
Dau coroana !!...

Answer 1

a) (2x-1)(2x+1)-4(x-2)²+17=
=(4x²+2x-2x-1)-4(x²-4x+4)+17=
=(4x²-1)-4x²+16x-16+17=
=4x²-1-4x²+16x+1=
=16x
b)3(x-1)²-5(x-1)(x+1)+2(x+1)²=
=3(x-1)²-5(x²-1)+2(x+1)²=
=3(x²-2x+1)-5x²+5+2(x²+2x+1)=
=3x²-6x+3-5x²+5+2x²+4x+2=
=-2x+10=
=-2(x+5)

c)(3x-2)²-3x(x-4)-(2-x)(2+x)=
=9x²-12x+4-3x²+12x-(2²-x²)=
=9x²+4-3x²-(4-x²)=
=6x²+4-4+x²=
=6x²+x²=7x²

d)(4x+3)²-(3x+4)²-7(x-1)(x+1)=
=16x²+24x+9-(9x²+24x+16)-7(x²-1)=
=16x²+24x+9-9x²-24x-16-7x²+7=
=16x²+9-9x²-16-7x²+7=
=5x²-7x²-5+7=
=-2x+2=
=-2(x-1)

e)(x+√2)²+(x-√3)²+(x-√2)²+(x+√3)²-(2x-√10)²=
=(x+√2)²+(x-√2)²+(x-√3)²+(x-√3)²-(2x-√10)²=
=x²+2x√2+2+x²-2x√2+2+(x-√3)²+(x+√3)²-(2x-√10)²=
=2x²+4+x²-2x√3+3+x²+2x√3+3-(2x-√10)²=
=2x²+4+2x²+6-(2x-√10)²=
=4x²+10-(2x-√10)²=
=4x²+10-(4x²-2×2x×√10+10)=
=4x²+10-(4x²-4x√10+10)=
=4x²+10-4x²+4x√10-10=
=4x√10