Question

Oblicz wartość liczbową wyrażenia

a) 2(x-3y)²-3(x-2y)(x+2y)+12xy dla x=3 i y=-1

b) (2x-3y)²-x(4x+3y)-9y² dla x=√5-3 i y=√5+3

Answer 1

a) 2(x-3y)²-3(x-2y)(x+2y)+12xy =2(x² - 6xy + 9y²) -3(x² - 2y²) + 12xy = 2x² - 12xy + 18y² - 3x² - 6y² + 12xy = -x² + 12y²=

-3² - 12² = 9 - 144 = -135

b) (2x-3y)²-x(4x+3y)-9y²  = (4x² - 12xy + 9y²) - (4x² +3xy) -9y² = 4x² - 12xy + 9y² - 4x² -3xy - 9y² = -15xy = -15(√5-3)(√5+3) = -15(5 - 9) = (-15)*(-4) = 60

Answer 2

a) 2(x-3y)²-3(x-2y)(x+2y)+12xy= 2(x-3y)*(x-3y)-3(x-2y)(x+2y)+12xy= 2(x²-3xy-3xy+9y²)-3(x²+2xy-2xy-4y²)+12xy=2(x²-9xy+9y²)-3(x²-4y²)=2x²-18xy+18y²-3x²+12y²=-x²-18xy+30y²=

=-3²-18*3*1+30*1²=-9-54+30=-33