∣x^2 −3x−4∣ = ∣x−4∣ ⇒ x=?


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 146914 by mathdanisur last updated on 16/Jul/21

$∣ x^{2} - 3 x - 4 ∣ = ∣ x - 4 ∣ \Rightarrow x = ?$
	Answered by liberty last updated on 16/Jul/21

	$∣ a ∣=∣ b ∣ \Leftrightarrow (a + b) (a - b) = 0$ $\Rightarrow (x^{2} - 3 x - 4 + x - 4) (x^{2} - 3 x - 4 - x + 4) = 0$ $\Rightarrow (x^{2} - 2 x - 8) (x^{2} - 4 x) = 0$ $\Rightarrow (x - 4) (x + 2) x (x - 4) = 0$ $\Rightarrow x (x + 2) {(x - 4)}^{2} = 0$ $\Rightarrow x = - 2; x = 0; x = 4$
	Commented by mathdanisur last updated on 16/Jul/21

	$t h a n k y o u S e r$
	Answered by Rasheed.Sindhi last updated on 17/Jul/21
	$∣x^2 −3x−4∣ = ∣x−4∣ ⇒ x=? { ((x^2 −3x−4=+(x−4))),(( OR)),((x^2 −3x−4=−(x−4))) :} { ((x^2 −4x=0⇒x(x−4)=0)),(( OR)),((x^2 −2x−8=0⇒(x−4)(x+2)=0)) :} x=0, −2, 4$
	$∣ x^{2} - 3 x - 4 ∣ = ∣ x - 4 ∣ \Rightarrow x = ?$ ${\begin{cases} x^{2} - 3 x - 4 = + (x - 4) \\ OR \\ x^{2} - 3 x - 4 = - (x - 4) \end{cases}$ ${\begin{cases} x^{2} - 4 x = 0 \Rightarrow x (x - 4) = 0 \\ OR \\ x^{2} - 2 x - 8 = 0 \Rightarrow (x - 4) (x + 2) = 0 \end{cases}$ $x = 0, - 2, 4$
	Commented by mathdanisur last updated on 18/Jul/21

	$T h a n k y o u S i r$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum