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COMC 2008 QB2

Problem Statement

(a) Determine all real numbers x such that (x+3)(x6)=14

(b) Determine all real numbers x such that 22x3(2x)4=0

(c) Determine all real numbers x such that (x23x)2=43(3xx2)

Problem Link

Solution (a) (x+3)(x6)=14 x23x4=0 (x4)(x+1)=0 x4=0x=4 x+1=0x=1 (b) 22x3(2x)4=0 (2x)23(2x)4=0 (2x4)(2x+1)=0 2x4=0x=2 2x+1=0no solution (c) (x23x)2=43(3xx2) Sub y=x23x:y23y4=0 (y4)(y+1)=0 y4=0x23x4=0 (x4)(x+1)=0x{1,4} y+1=0x23x+1=0 x=(3)±(3)24(1)(1)2(1) x=3±52 x{1,4,3+52,352}
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