Question

Uprość wyrażenie o oblicz jego wartość: a) (x-1)^2-(x-1)*(x+2) dla x=√3-1 b) (x+3)^2-(x-3)^2-12 dla x=√2+1 c) (x-4y)^2 - (4y+x)^2 dla x=1/4 y= √3/4

Answer 1

a) (x-1)^2-(x-1)*(x+2) = x²-2x+1-(x²+2x-x-2) = x²-2x+1-x²-x+2 =-3x+3

x=√3-1

-3(√3-1) +3 = -3√3+6 = -3(√3-2)

 

 

(x+3)^2-(x-3)^2-12 = x²+6x+9-x²+6x-9-12 = 12x-12

x=√2+1

12(√2+1)-12 = 12√2+12-12 = 12√2

 

 

(x-4y)^2 - (4y+x)^2 = x²-8xy+16y² - 16y²-8xy-x² = -16xy

x=1/4 y= √3/4

 

-16(1/4 * √3/4) = -16 * √3/16 = -√3

 

Answer 2

a)

 

b)

 

c)