{"@context":"https://schema.org/","@type":"Quiz","about":{"@type":"Thing","name":"Number System"},"educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"Maths"}],"hasPart":[{"@context":"https://schema.org/","@type":"Question","eduQuestionType":"Flashcard","text":"|x-3|^(3x^2 - 10x + 3) = 1. Find x. - ReadAxis","acceptedAnswer":{"@type":"Answer","text":"There can be three cases:CASE I : 3x2–10x+3=0 and |x−3|≠03x2–10x+3=0 and x−3≠0⇒3x2–9x–x+3=0 and x≠3⇒3x(x–3)–1(x–3)=0 and x≠3⇒(3x–1)(x–3)=0 and x≠3x=13 or x=3 and x≠3Therefore from CASE I , x=13CASE II : |x–3|=1x−3±1⇒x=4 OR x=2From CASE II , x=4,x=2CASE III : |x–3|=−1 and 3x2–10x+3 is an even number or is equal to 0But |x–3|=−1 is not possible.Hence we get x∈{13,4,2}"}}]}{"@context":"http://schema.org","@type":"QAPage","name":"|x-3|^(3x^2 - 10x + 3) = 1. Find x. - ReadAxis","description":"There can be three cases:CASE I : 3x2–10x+3=0 and |x−3|≠03x2–10x+3=0 and x−3≠0⇒3x2–9x–x+3=0 and x≠3⇒3x(x–3)–1(x–3)=0 and x≠3⇒(3x–1)(x–3)=0 and x≠3x=13 or x=3 and x≠3Therefore from CASE I , x=13CASE II : |x–3|=1x−3±1⇒x=4 OR x=2From CASE II , x=4,x=2CASE III : |x–3|=−1 and 3x2–10x+3 is an even number or is equal to 0But |x–3|=−1 is not possible.Hence we get x∈{13,4,2}","mainEntity":{"@type":"Question","@id":"https://readaxis.com/question-answer/x-33x2-10x-3-1-find-x/","name":"|x-3|^(3x^2 - 10x + 3) = 1. Find x. - ReadAxis","text":"|x-3|^(3x^2 - 10x + 3) = 1. Find x. - ReadAxis","dateCreated":"2023-01-21T05:48:00.997Z","answerCount":"1","author":{"@type":"Person","name":"ReadAxis","url":"https://www.readaxis.com/"},"acceptedAnswer":{"@type":"Answer","upvoteCount":"4","text":"There can be three cases:CASE I : 3x2–10x+3=0 and |x−3|≠03x2–10x+3=0 and x−3≠0⇒3x2–9x–x+3=0 and x≠3⇒3x(x–3)–1(x–3)=0 and x≠3⇒(3x–1)(x–3)=0 and x≠3x=13 or x=3 and x≠3Therefore from CASE I , x=13CASE II : |x–3|=1x−3±1⇒x=4 OR x=2From CASE II , x=4,x=2CASE III : |x–3|=−1 and 3x2–10x+3 is an even number or is equal to 0But |x–3|=−1 is not possible.Hence we get x∈{13,4,2}","url":"https://readaxis.com/question-answer/x-33x2-10x-3-1-find-x/","dateCreated":"2023-01-21T05:48:00.997Z","author":{"@type":"Person","name":"Readaxis Admin"}},"suggestedAnswer":[]}}

Question

$$|x-3|^{3x^2 – 10x + 3} = 1$$. Find $$x$$.

Solution:

There can be three cases:

CASE I : $$3x^2 – 10x + 3 = 0$$ and $$|x-3| \neq 0$$

$$3x^2 – 10x + 3 = 0$$ and $$x-3 \neq 0$$
$$\Rightarrow 3x^2 – 9x – x + 3 = 0$$ and $$x \neq 3$$
$$\Rightarrow 3x(x – 3) – 1(x – 3) = 0$$ and $$x \neq 3$$
$$\Rightarrow (3x – 1)(x – 3) = 0$$ and $$x \neq 3$$
$$x = \frac{1}{3}$$ or $$x = 3$$ and $$x \neq 3$$

Therefore from CASE I , $$x = \frac{1}{3}$$

CASE II : $$|x – 3| = 1$$

$$x\;-\;3 \pm 1$$
$$\Rightarrow x = 4$$ OR $$x = 2$$

From CASE II , $$x = 4 , x = 2$$

CASE III : $$|x – 3| = -1$$ and $$3x^2 – 10x + 3$$ is an even number or is equal to 0

But $$|x – 3| = -1$$ is not possible.

Hence we get $$x \in \{\frac{1}{3} , 4 , 2 \}$$

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