If a − (4/( (√a))) = 17 Find a − 4 (√a) = ?


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 184438 by Shrinava last updated on 06/Jan/23

$If a - \frac{4}{\sqrt{a}} = 17$ $Find a - 4 \sqrt{a} = ?$
	Answered by Frix last updated on 06/Jan/23

	$a - \frac{4}{\sqrt{a}} = 17$ $Let t = \sqrt{a} \Rightarrow t > 0$ $t^{3} - 17 t - 4 = 0$ $(t + 4) (t - 2 - \sqrt{5}) (t - 2 + \sqrt{5}) = 0$ $t > 0 \Rightarrow t = 2 + \sqrt{5}$ $\Rightarrow$ $a - 4 \sqrt{a} = 1$
	Answered by Frix last updated on 06/Jan/23

	$a - \frac{4}{\sqrt{a}} = 17 \Rightarrow a = \frac{4}{\sqrt{a}} + 17 (1)$ $a - 4 \sqrt{a} = x \Rightarrow a = 4 \sqrt{a} + x (2)$ $(2) - (1)$ $\frac{4 a + (x - 17) \sqrt{a} - 4}{\sqrt{a}} = 0$ $4 a + (x - 17) \sqrt{a} - 4 = 0$ $[a = 4 \sqrt{a} + x]$ $(t + 4) (x - 1) = 0 \Rightarrow x = 1$
	Answered by a.lgnaoui last updated on 06/Jan/23
	$((a(√a) −4)/( (√a)))=17 a−((4(√a))/a)=17⇒ 4(√a)=a^2 −17a a−4(√a) =18a−a^2 calcul de a 16a=(a^2 −17a)^2 (a^2 −17a−4(√a) )(a^2 −17a+4(√a) )=0 (((√a) )^3 −17((√a) )−4)((√a) )^3 −17(√a) +4)=0 (√a) =z { ((z^3 −17z−4=0)),((z^3 −17z+4=0)) :} .......z? avec a>0 ⇒ a−4(√a) =z^2 −4z$
	$\frac{a \sqrt{a} - 4}{\sqrt{a}} = 17$ $a - \frac{4 \sqrt{a}}{a} = 17 \Rightarrow 4 \sqrt{a} = a^{2} - 17 a$ $a - 4 \sqrt{a} = 18 a - a^{2}$ $c a l c u l d e a$ $16 a = {(a^{2} - 17 a)}^{2}$ $(a^{2} - 17 a - 4 \sqrt{a}) (a^{2} - 17 a + 4 \sqrt{a}) = 0$ $({(\sqrt{a})}^{3} - 17 (\sqrt{a}) - 4) {(\sqrt{a})}^{3} - 17 \sqrt{a} + 4) = 0$ $\sqrt{a} = z$ ${\begin{cases} z^{3} - 17 z - 4 = 0 \\ z^{3} - 17 z + 4 = 0 \end{cases}$ $. . . . . . . z ? a v e c a > 0$ $\Rightarrow a - 4 \sqrt{a} = z^{2} - 4 z$
	Commented by a.lgnaoui last updated on 06/Jan/23

	$z^{3} - 17 z - 4 = 0 (z = 4, 236067)$ $s i t a - 4 \sqrt{a} = 1$ $z^{3} - 17 z + 4 s o i t z = 4$ $a - 4 \sqrt{a} = 0$
	Commented by Frix last updated on 06/Jan/23

	$z = \sqrt{a} \Leftrightarrow a = z^{2}$ $z = 4 \Rightarrow a = 16$ $a - \frac{4}{\sqrt{a}} = 16 - 1 = 15 \neq 17$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum