Arbeitsblatt Gleichungen lösen Teil 2

Question

3e)  (p+5)²-(p-3)²  = 12(p+4)

         p²+10p+10-p²-6p+6   =   12p+48

         4p+16       = 12p+48

         16           =     8p+48

         -32     =    8p

         -4        =    p

3f)  (2p+3)²-(p-4)²+18  =  3(p²+2)-5

       4p²+10p+6-p²-8p+8+18   =   3p²+6-5

         3p²+2p+32     =   3p²+1

2p+32   =   1           /   2p   =   -31     /    p   =  15 1/2           ???????

Answer 1

(p + 5)^2 - (p - 3)^2 = 12·(p + 4)

p^2 + 10·p + 25 - (p^2 - 6·p + 9) = 12·p + 48

p^2 + 10·p + 25 - p^2 + 6·p - 9 = 12·p + 48

16·p + 16 = 12·p + 48

4·p = 32

p = 8

Comments

(2·p + 3)^2 - (p - 4)^2 + 18 = 3·(p^2 + 2) - 5

4·p^2 + 12·p + 9 - (p^2 - 8·p + 16) + 18 = 3·p^2 + 6 - 5

3·p^2 + 20·p + 11 = 3·p^2 + 1

20·p = -10

p = -1/2