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Question Number 146606 by iloveisrael last updated on 14/Jul/21

Answered by som(math1967) last updated on 14/Jul/21

x+(√(x^2 −1))+(1/(x−(√(x^2 −1))))=20 ((x^2 −x^2 +1+1)/(x−(√(x^2 −1))))=20 (1/(x−(√(x^2 −1))))=10 x−(√(x^2 −1))=(1/(10)) again (1/(x−(√(x^2 −1))))=10 ((x+(√(x^2 −1)))/(x^2 −x^2 +1))=10 x+(√(x^2 −1))=10 ∴2x=10+(1/(10))=((101)/(10)) x=((101)/(20)) now x^2 +(√(x^4 −1))+(1/(x^2 +(√(x^4 −1)))) x^2 +(√(x^4 −1)) +((x^2 −(√(x^4 −1)))/(x^4 −x^4 +1)) =2x^2 =2×(((101)/(20)))^2

x+x2−1+1x−x2−1=20x2−x2+1+1x−x2−1=201x−x2−1=10x−x2−1=110again1x−x2−1=10x+x2−1x2−x2+1=10x+x2−1=10∴2x=10+110=10110x=10120nowx2+x4−1+1x2+x4−1x2+x4−1+x2−x4−1x4−x4+1=2x2=2×(10120)2

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