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Question

Solve each of the following equations and also verify your solution :

(x + 2)(x+3)+(x-3)(x-2)-2x(x+1)=0


Solution

(x+2)(x+3)+(x3)(x2)2x(x+1)=0[x2+(2+3)x+2×3]+[x2+(32)x+(3)(2)]2x22x=0x2+5x+6+x25x+62x22x=0x2+x22x2+5x5x2x+6+6=0=2x+12=0
Substracting 12 from both sides,
2x+1212=0122x=12
Dividing by - 2,
2x2=122x=6x=6
Verification :
L.H.S.=(x+2)(x+3)+(x3)(x2)2x(x+1)=(6+2)(6+3)+(63)(62)2×6(6+1)=8×9+3×412×7=72+1284=8484=0=R.H.S.

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