I gimnazjum

Matematyka z plusem 1. Podręcznik

a) <img style="vertical-align: middle;" src="../../../math/formula?%5Cdisplaystyle%7B%5Cleft(%7Bx%7D%2B%7By%7D%5Cright)%7D%5Ccdot%7Ba%7D%2B%7B%5Cleft(%7Bx%7D%2B%7By%7D%5Cright)%7D%5Ccdot%7Bb%7D%3D%7B%5Cleft(%7Bx%7D%2B%7By%7D%5Cright)%7D%5Ccdot%7B%5Cleft(%7Ba%7D%2B%7Bb%7D%5Cright)%7D"> b) <img style="vertical-align: middle;" src="../../../math/formula?%5Cdisplaystyle%7B3%7D%7B%5Cleft(%7Bz%7D-%7By%7D%5Cright)%7D-%7Ba%7D%7B%5Cleft(%7Bz%7D-%7By%7D%5Cright)%7D%3D%7B%5Cleft(%7B3%7D-%7Ba%7D%5Cright)%7D%7B%5Cleft(%7Bz%7D-%7By%7D%5Cright)%7D"> c) <img style="vertical-align: middle;" src="../../../math/formula?%5Cdisplaystyle%7B%5Cleft(%7Bm%7D-%7B1%7D%5Cright)%7D%7B%5Cleft(%7Bk%7D-%7B1%7D%5Cright)%7D%2B%7B%5Cleft(%7Bk%7D-%7B1%7D%5Cright)%7D%7B%5Cleft(%7Bm%7D%2B%7B1%7D%5Cright)%7D%3D"> (k−1)(m−1+m+1)=(k−1)2m <img style="vertical-align: middle;" src="../../../math/formula?%5Cdisplaystyle%7Bd%7D%7B%5C)%7D%5C%20%7B%5Cleft(%7Ba%7D-%7B1%7D%5Cright)%7D%7B%5Cleft(%7Bb%7D%2B%7Bc%7D%5Cright)%7D-%7B%5Cleft(%7Ba%7D-%7B1%7D%5Cright)%7D%7B%5Cleft(%7Bb%7D-%7Bc%7D%5Cright)%7D%3D"> (a−1)(b+c−(b−c)=(a−1)(b+c−b+c)=2c(a−1)

Rozwiązanie 1

<img style="vertical-align: middle;" src="../../../math/formula?%5Cdisplaystyle%7Ba%7D%7B%5C)%7D%5C%20%7B%7Bx%7D%7D%5E%7B%7B2%7D%7D%2B%7B0%7D%2C%7B24%7D%7Bx%7D-%7B0%7D%2C%7B26%7D%3D%7Bx%7D%5Ccdot%7Bx%7D%2B%7B0%7D%2C%7B24%7D%5Ccdot%7Bx%7D-%7B0%7D%2C%7B26%7D%3D%7Bx%7D%7B%5Cleft(%7Bx%7D%2B%7B0%7D%2C%7B24%7D%5Cright)%7D-%7B0%7D%2C%7B26%7D"> dla x=0,76:  0,76⋅(0,76+0,24)−0,26=0,76⋅1−0,26=0,5

a) x+(x+1)+(x+2)=x+x+1+x+2=3x+3=3(x+1)

Neich x będzie liczbą dziesiątek a y liczbą jedności. Wtedy różnica:

8a2+4a3=a2⋅8+a2⋅4a=a2(8+4a)

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Matematyka z plusem 1. Podręcznik