Uzasadnij, że poniższa nierówność jest prawdziwa.
a) (x^2+1)^2 - 2(x^2+1)(x^2-1) + (x^2-1)^2 = 4
b) (x+1)^3 - (x-1)^3 -6(x+1)(x-1) = 8
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a)
(x²+1)² - 2(x²+1)(x²-1) + (x²-1)² = 4
L= x⁴+2x²+1-2(x⁴-1)+x⁴-2x²+1=2x⁴+2 -2x₄+2=4=P
b)
(x+1)³ - (x-1)³ -6(x+1)(x-1) = 8
L=x³+3x²+3x+1-(x³-3x²+3x-1)-6(x²-1)=x³+3x²+3x+1-x³+3x²-3x+1-6x²+6=x³-x³+3x²+3x²-6x²+3x-3x+1+1+6=8=P