Question

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a) + 4 x ^2 + 5 = ( x + 1 )^3

b) x(x + 1)^2 -( x + 2)^3 = - 10x - 3x^2 - 8

Answer 1

a]  (x-1)^3 +4x^2 + 5 = (x+1)^3

       x^3-3x^2+3x-1+4x^2+5= x^3 +3x^2 + 3x + 1

     x^3-x^3 -3x^2 +4x^2-3x^2+3x-3x-1+5-1=0

     -2x^2+3=0

     -2x^2=-3

         x^2=3/2

         x=-v3/2    U    x=v3/2

 

b]

x(x+1)^2 - (x+2)^3 = -10 -3x^2 -8

x(x^2+2x+1)-(x^3+6x^2 + 12x + 8 )=-10-3x^2-8

x^3+2x^2+x-x^3-6x^2-12x-8=-10x-3x^2-8

-x^2+x=-8+8

-x^2-x=0

-x(x+1)=0

-x=0               x+1=0

x=0    U              x=-1

Answer 2

a) (x-1)³ + 4 x² + 5 = ( x + 1 )³

x³-3x²+3x-1 +4x²+5=x³+3x²+3x+1

x²+3x+4=3x²+3x+1

-2x²=-3

2x²=3

 

 

 

 

b) x(x + 1)² -( x + 2)³ = - 10x - 3x² - 8

x(x²+2x+1) - (x³+6x²+12x+8)= -10x - 3x²-8

x³ + 2x² + x - x³ - 6x² - 12x - 8 = -3x² - 10x - 8

-4x² - 11x = -3x² - 10 x 

-x² -x =0

x(-x-1)=0

x=0 ∨ x=-1