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intercepts of x^3

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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2x²−6x+3<0

Solution

−√3+32 <x<√3+32

Interval Notation

(−√3+32 , √3+32 )

Decimal

0.63397…<x<2.36602…

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Solution steps

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2x²−6x+3<0

Complete the square 2x²−6x+3: 2(x−32 )²−32

2(x−32 )²−32 <0

Move 32 to the right side

2(x−32 )²<32

Divide both sides by 2

(x−32 )²<34

For uⁿ < a, if n is even then −ⁿ√a < u < ⁿ√a

−√34 <x−32 <√34

If a<u<b then a<u and u<b

−√34 <x−32 and x−32 <√34

−√34 <x−32 : x>−√3+32

x−32 <√34 : x<√3+32

Combine the intervals

x>−√3+32 and x<√3+32

Merge Overlapping Intervals

−√3+32 <x<√3+32

Number Line

−√3+32 <x<√3+32

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

intercepts of x^3

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