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Question Number 195175 by valdirmd last updated on 25/Jul/23

Answered by Rasheed.Sindhi last updated on 26/Jul/23

x^4 +x^2 =11/5 , (((x+1)/(x−1)))^(1/3) +(((x−1)/(x+1)))^(1/3) =? ▶Let y=(((x+1)/(x−1)))^(1/3) +(((x−1)/(x+1)))^(1/3) y^3 =((x+1)/(x−1))+((x−1)/(x+1))+3y y^3 −3y=((x^2 +2x+1+x^2 −2x+1)/(x^2 −1)) y^3 −3y=2(((x^2 −1+2)/(x^2 −1)))=2(1+(2/(x^2 −1))) =2+(4/(x^2 −1)) ▶ x^4 +x^2 =11/5⇒5x^4 +5x^2 −11=0 x^2 (≥0)=((−5+(√(25+220)))/(10))=((−5+7(√5))/(10)) ▶y^3 −3y=2+(4/(x^2 −1))=2+(4/(((−5+7(√5))/(10))−1)) =2+(4/((−15+7(√5) )/(10)))=2+((40)/(−15+7(√5) )) =2+((40(−15−7(√5) ))/(225−245)) y^3 −3y =2−2(−15−7(√5) ) =2+30+14(√5) = y^3 −3y=32+14(√5) ▶(((x+1)/(x−1)))^(1/3) +(((x−1)/(x+1)))^(1/3) =y=3.7361626

x4+x2=11/5,(x+1x−1)1/3+(x−1x+1)1/3=?▸Lety=(x+1x−1)1/3+(x−1x+1)1/3y3=x+1x−1+x−1x+1+3yy3−3y=x2+2x+1+x2−2x+1x2−1y3−3y=2(x2−1+2x2−1)=2(1+2x2−1)=2+4x2−1▸x4+x2=11/5⇒5x4+5x2−11=0x2(⩾0)=−5+25+22010=−5+7510▸y3−3y=2+4x2−1=2+4−5+7510−1=2+4−15+7510=2+40−15+75=2+40(−15−75)225−245y3−3y=2−2(−15−75)=2+30+145=y3−3y=32+145▸(x+1x−1)1/3+(x−1x+1)1/3=y=3.7361626

Commented by Rasheed.Sindhi last updated on 26/Jul/23

ThanX sir! I′m going to correct my answer.

ThanXsir!I′mgoingtocorrectmyanswer.

Commented by jihamine2301 last updated on 26/Jul/23

Error at y^3 =.....+3y and x^2 should get only positive value

Erroraty3=.....+3yandx2shouldgetonlypositivevalue

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