Solution Found!
Is this reasoning for finding the solutions of the
Chapter 7, Problem 34E(choose chapter or problem)
Is this reasoning for finding the solutions of the equation \(\sqrt{2 x^{2}-1}=x\) correct? \((1) \sqrt{2 x^{2}-1}=x\) is given; (2) \(2 x^{2}-1=x^{2}\), obtained by squaring both sides of (1); (3) \(x^{2}-1=0\), obtained by subtracting \(x^{2}\) from both sides of \((2) ;(4)(x-1)(x+1)=0\), obtained by factoring the left-hand side of \(x^{2}-1 ;(5) x=1\) or \(x=-1\), which follows because \(a b=0\) implies that \(a=0\) or \(b=0\).
Equation Transcription:
(2) 2x2 − 1 = x2
(1); (3) x2 − 1 = 0
x2 − 1; (5) x = 1 or x = −1
Text Transcription:
Square root 2x^2-1=x
(2) 2x^2 − 1 = x2^
(1); (3) x2 − 1 = 0
x^2 − 1; (5) x = 1 or x = −1
Questions & Answers
QUESTION:
Is this reasoning for finding the solutions of the equation \(\sqrt{2 x^{2}-1}=x\) correct? \((1) \sqrt{2 x^{2}-1}=x\) is given; (2) \(2 x^{2}-1=x^{2}\), obtained by squaring both sides of (1); (3) \(x^{2}-1=0\), obtained by subtracting \(x^{2}\) from both sides of \((2) ;(4)(x-1)(x+1)=0\), obtained by factoring the left-hand side of \(x^{2}-1 ;(5) x=1\) or \(x=-1\), which follows because \(a b=0\) implies that \(a=0\) or \(b=0\).
Equation Transcription:
(2) 2x2 − 1 = x2
(1); (3) x2 − 1 = 0
x2 − 1; (5) x = 1 or x = −1
Text Transcription:
Square root 2x^2-1=x
(2) 2x^2 − 1 = x2^
(1); (3) x2 − 1 = 0
x^2 − 1; (5) x = 1 or x = −1
ANSWER:
Solution :
Step 1:
In this problem we have to find some conditions from the given value