Question Number 149240 by john_santu last updated on 04/Aug/21

solve for real number x^4 −3x^2 +1 =(√((4/(4−x^2 )) −1))

Answered by MJS_new last updated on 04/Aug/21

x=±(√t)∧t≥0 t^2 −3t+1=(√(t/(4−t))) squaring & transforming t^5 −10t^4 +35t^3 −50t^2 +26t−4=0 (t−2)(t^2 −4t+1)(t^2 −4t+2)=0 testing all solutions I get t_1 =2−(√3) ⇒ x=±(((√6)−(√2))/2) t_2 =2+(√2) ⇒ x=±(√(2+(√2))) t_3 =2+(√3) ⇒ x=±(((√6)+(√2))/2)

Commented byjohn_santu last updated on 04/Aug/21

hello prof. how are you?

Commented byMJS_new last updated on 04/Aug/21

thank you, I′m ok. and what about you?

Commented byjohn_santu last updated on 05/Aug/21

I′m ok too .. prof