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simlify-A-1-2-5-4-1-2-5-4-B-1-3-2-6-1-3-2-6-

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Question Number 38517 by math khazana by abdo last updated on 26/Jun/18
simlify A= (1/((2−(√5))^4 )) + (1/((2+(√5))^4 )) B = (1/((3−(√2))^6 )) +(1/((3+(√2))^6 ))
simlifyA=1(2−5)4+1(2+5)4B=1(3−2)6+1(3+2)6
Answered by MJS last updated on 26/Jun/18
A=(((2+(√5))^4 +(2−(√5))^4 )/((2−(√5))^4 (2+(√5))^4 ))=(((9+4(√5))^2 +(9−4(√5))^2 )/(((2−(√5))(2+(√5)))^4 ))= =((81+72(√5)+80+81−72(√5)+80)/((4−5)^4 ))=322 B=(((3+(√2))^6 +(3−(√2))^6 )/((3−(√2))^6 (3+(√2))^6 ))=(((11+6(√2))^3 +(11−6(√2))^3 )/(((3−(√2))(3+(√2)))^6 ))= =((1331+2178(√2)+2376+432(√2)+1331−2178(√2)+2376−432(√2))/((9−2)^(6q) ))= =((7414)/(117649))
A=(2+5)4+(2−5)4(2−5)4(2+5)4=(9+45)2+(9−45)2((2−5)(2+5))4==81+725+80+81−725+80(4−5)4=322B=(3+2)6+(3−2)6(3−2)6(3+2)6=(11+62)3+(11−62)3((3−2)(3+2))6==1331+21782+2376+4322+1331−21782+2376−4322(9−2)6q==7414117649
Commented by math khazana by abdo last updated on 26/Jun/18
thank you sir.
thankyousir.
Answered by math1967 last updated on 27/Jun/18
let x=(1/(2−(√5)))=−(2+(√5) ) y=(1/(2+(√5)))=−(2−(√5)) ∴xg=(4−5)=−1 x+g=−4 ∴x^4 +y^4 ={(x+y)^2 −2xy}^2 −2x^2 y^2 ={16+2}^2 −2=324−2=322
letx=12−5=−(2+5)y=12+5=−(2−5)∴xg=(4−5)=−1x+g=−4∴x4+y4={(x+y)2−2xy}2−2x2y2={16+2}2−2=324−2=322

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