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Question Number 12361 by Joel576 last updated on 20/Apr/17

((√2) +(√3) +2 + (√5))(−(√2) + (√3) + 2 − (√5))((√(10)) + 2(√3)) Can you solve this without solving them manually?

(2+3+2+5)(−2+3+2−5)(10+23)Canyousolvethiswithoutsolvingthemmanually?

Answered by ajfour last updated on 20/Apr/17

(a+b+c+d)(b+c−a−d)(ad+bc) =[(b+c)^2 −(a+d)^2 ](ad+bc) =[b^2 +c^2 −a^2 −d^2 +2(bc−ad)](ad+bc) =[b^2 +c^2 −a^2 −d^2 ](ad+bc)+2(b^2 c^2 −a^2 d^2 ) =0+2(12−10) =4 .

(a+b+c+d)(b+c−a−d)(ad+bc)=[(b+c)2−(a+d)2](ad+bc)=[b2+c2−a2−d2+2(bc−ad)](ad+bc)=[b2+c2−a2−d2](ad+bc)+2(b2c2−a2d2)=0+2(12−10)=4.

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