zadanie w załączniku
nierówności
a)
b)
c)
a) x=√3 +1
(x-1)² - (x-1)(x+3) = (x-1) ( x-1 -x -3) = (x-1) ( -4) = (√3 +1 -1)(-4) = -4√3
b) x=√2 +1
(x+3)² - (x-3)² - 12 = (x+3 + x -3)(x+3 - x +3) -12 = 2x *6 -12 = 12x -12 = 12(x-1) = 12(√2 +1 -1)
= 12√2
c) x=√2 y=√8
(2x + 3y)(2x - 3y)- (2x-3y)² = (2x-3y)(2x+3y - 2x +3y) = (2x -3y)6y = 12xy -18y² =
= 12 √2 √8 - 18(√8)² = 12√16 - 18*8 = 12*4 - 144 = -96
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a)
b)
c)
a) x=√3 +1
(x-1)² - (x-1)(x+3) = (x-1) ( x-1 -x -3) = (x-1) ( -4) = (√3 +1 -1)(-4) = -4√3
b) x=√2 +1
(x+3)² - (x-3)² - 12 = (x+3 + x -3)(x+3 - x +3) -12 = 2x *6 -12 = 12x -12 = 12(x-1) = 12(√2 +1 -1)
= 12√2
c) x=√2 y=√8
(2x + 3y)(2x - 3y)- (2x-3y)² = (2x-3y)(2x+3y - 2x +3y) = (2x -3y)6y = 12xy -18y² =
= 12 √2 √8 - 18(√8)² = 12√16 - 18*8 = 12*4 - 144 = -96