Question

Ex 23si28Va roggg coroannnaaaa

Answer 1

23. a. x²-7-(x²+2x+1)=x²-7-x²-2x-1=-2x-8=-2(x+4)
b. 5x²+6√5x+9-(20x²-3)+45x²-6√5x+1=
=5x²+9-20x²+3+45x²+1=
=30x²+13
c.4x²-4x√3+3+12x²+4√3x+1-(27x²-7)=
=4x²+3+12x²+1-27x²+7=
=-11x²+11=-11(x²-1)=-11(x-1)(x+1)
d. 3x²-4√3x+4+12+4√3x+x²+5x²-16=
=9x²
e. 9-6√2x+2x²+6+6√3x+3x²-(15-2x²)=
=15+5x²-15+2x²=7x²
f. a²-3+a²-5-(a²-7)=
=2a²-8-a²+7=
=a²-1=(a-1)(a+1)

28. x-1/x=3
a.(x-1/x)²=9
x²-2+1/x²=9
x²+1/x²=11
b. (x-1/x)³=27
x³-3x²·1/x+3x·1/x²-1/x³=27
x³-3x+3/x-1/x³=27
x³-3(x-1/x)-1/x³=27
x³-3·3-1/x³=27
x³-1/x³=27+9
x³-1/x³=36
c. (x-1/x)²(x-1/x)²=81
(x²-2+1/x²)²=81
x^4+4+1/(x^4)-4x²+2-4/x²=81
x^4+1/(x^4)+6-4(x²+1/x²)=81
x^4+1/(x^4)-4(x²+1/x²)=75

x²+1/x²=11 (de la punctul a)
x^4+1/x^4=75+44
x^4+1/x^4=119