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Question

Simplify:

(i) 5+353+535+3

(ii) 12+3+253+125

(iii) 25+3+13+235+2

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Solution

(i) 5+353+535+3=(5+3)2+(53)2(53)(5+3)=2[(5)2+(3)2](5)2(3)2 {(a+b)2+(ab)2=2(a2+b2)}=2(5+3)53=2×82=8

(ii) 12+3=1(23)(2+3)(23)=1(23)(2)2(3)2=2343=231=23253=2(5+3)(53)(5+3)=2(5+3)(5)2(3)2=2(5+3)53=2(5+3)2=5+3125=1(2+5)(25)(2+5)=2+5(2)2(5)2=2+545=2+51=(25)Now, 12+3+253+125=(23)+(5+3)+(25)=23+5+325=0

(iii) 25+3=2(53)(5+3)(53)=2(53)(5)2(3)2=2(53)53=2(53)2=5313+2=1×(32)(3+2)(32)=32(3)2(2)2=3232=321=3235+2=3(52)(5+2)(52)=3(52)(5)2(2)2=3(52)52=3(52)3=52Now, 22+3+13+235+2=53+32(52)=53+325+2=0


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