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If-a-4-a-17-Find-a-4-a-

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Question Number 184438 by Shrinava last updated on 06/Jan/23
If a − (4/( (√a))) = 17 Find a − 4 (√a) = ?
Ifa−4a=17Finda−4a=?
Answered by Frix last updated on 06/Jan/23
a−(4/( (√a)))=17 Let t=(√a) ⇒ t>0 t^3 −17t−4=0 (t+4)(t−2−(√5))(t−2+(√5))=0 t>0 ⇒ t=2+(√5) ⇒ a−4(√a)=1
a−4a=17Lett=a⇒t>0t3−17t−4=0(t+4)(t−2−5)(t−2+5)=0t>0⇒t=2+5⇒a−4a=1
Answered by Frix last updated on 06/Jan/23
a−(4/( (√a)))=17 ⇒ a=(4/( (√a)))+17 (1) a−4(√a)=x ⇒ a=4(√a)+x (2) (2)−(1) ((4a+(x−17)(√a)−4)/( (√a)))=0 4a+(x−17)(√a)−4=0 [a=4(√a)+x] (t+4)(x−1)=0 ⇒ x=1
a−4a=17⇒a=4a+17(1)a−4a=x⇒a=4a+x(2)(2)−(1)4a+(x−17)a−4a=04a+(x−17)a−4=0[a=4a+x](t+4)(x−1)=0⇒x=1
Answered by a.lgnaoui last updated on 06/Jan/23
((a(√a) −4)/( (√a)))=17 a−((4(√a))/a)=17⇒ 4(√a)=a^2 −17a a−4(√a) =18a−a^2 calcul de a 16a=(a^2 −17a)^2 (a^2 −17a−4(√a) )(a^2 −17a+4(√a) )=0 (((√a) )^3 −17((√a) )−4)((√a) )^3 −17(√a) +4)=0 (√a) =z { ((z^3 −17z−4=0)),((z^3 −17z+4=0)) :} .......z? avec a>0 ⇒ a−4(√a) =z^2 −4z
aa−4a=17a−4aa=17⇒4a=a2−17aa−4a=18a−a2calculdea16a=(a2−17a)2(a2−17a−4a)(a2−17a+4a)=0((a)3−17(a)−4)(a)3−17a+4)=0a=z{z3−17z−4=0z3−17z+4=0…….z?aveca>0⇒a−4a=z2−4z
Commented by a.lgnaoui last updated on 06/Jan/23
z^3 −17z−4=0 (z=4,236067) sit a−4(√a) =1 z^3 −17z+4 soit z=4 a−4(√a) =0
z3−17z−4=0(z=4,236067)sita−4a=1z3−17z+4soitz=4a−4a=0
Commented by Frix last updated on 06/Jan/23
z=(√a) ⇔ a=z^2 z=4 ⇒ a=16 a−(4/( (√a)))=16−1=15≠17
z=a⇔a=z2z=4⇒a=16a−4a=16−1=15≠17

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