how to simplify and solve this equation :
Multi tool use
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Solve this equation for $x$:
$$left|x sqrt{1-x^2} +x right| = sqrt{1+x^2}$$
I'm having a problem getting rid of the square root!
algebra-precalculus problem-solving absolute-value
edited Nov 21 at 12:17
amWhy
191k27223438
asked Nov 21 at 11:54
Amr Samir
101
New contributor
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add a comment |
up vote
-3
down vote
favorite
Solve this equation for $x$:
$$left|x sqrt{1-x^2} +x right| = sqrt{1+x^2}$$
I'm having a problem getting rid of the square root!
algebra-precalculus problem-solving absolute-value
edited Nov 21 at 12:17
amWhy
191k27223438
asked Nov 21 at 11:54
Amr Samir
101
New contributor
Amr Samir is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Use LaTeX to write
– ramanujan
Nov 21 at 12:01
add a comment |
up vote
-3
down vote
favorite
up vote
-3
down vote
favorite
Solve this equation for $x$:
$$left|x sqrt{1-x^2} +x right| = sqrt{1+x^2}$$
I'm having a problem getting rid of the square root!
algebra-precalculus problem-solving absolute-value
edited Nov 21 at 12:17
amWhy
191k27223438
asked Nov 21 at 11:54
Amr Samir
101
New contributor
Amr Samir is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Solve this equation for $x$:
$$left|x sqrt{1-x^2} +x right| = sqrt{1+x^2}$$
I'm having a problem getting rid of the square root!
algebra-precalculus problem-solving absolute-value
algebra-precalculus problem-solving absolute-value
edited Nov 21 at 12:17
amWhy
191k27223438
asked Nov 21 at 11:54
Amr Samir
101
New contributor
Amr Samir is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 21 at 12:17
amWhy
191k27223438
asked Nov 21 at 11:54
Amr Samir
101
New contributor
Amr Samir is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 21 at 12:17
amWhy
191k27223438
edited Nov 21 at 12:17
amWhy
191k27223438
edited Nov 21 at 12:17
amWhy
191k27223438
191k27223438
asked Nov 21 at 11:54
Amr Samir
101
New contributor
Amr Samir is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 21 at 11:54
Amr Samir
101
asked Nov 21 at 11:54
Amr Samir
101
101
New contributor
Amr Samir is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Amr Samir is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Amr Samir is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Use LaTeX to write
– ramanujan
Nov 21 at 12:01
add a comment |
1
Use LaTeX to write
– ramanujan
Nov 21 at 12:01
1
1
Use LaTeX to write
– ramanujan
Nov 21 at 12:01
Use LaTeX to write
– ramanujan
Nov 21 at 12:01
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
Provided $-1le xle 1$, you get:
begin{align}
left|x sqrt{1-x^2} +x right| = sqrt{1+x^2}\
left|x left(sqrt{1-x^2} +1right) right| = sqrt{1+x^2}\
|x|left(sqrt{1-x^2} +1right) = sqrt{1+x^2}\
x^2left(sqrt{1-x^2} +1right)^2 = 1+x^2\
x^2left(1-x^2+2sqrt{1-x^2}+1right) = 1+x^2\
2x^2sqrt{1-x^2}=x^4-x^2+1\
4x^4left(1-x^2right)=left(x^4-x^2+1right)^2
end{align}
answered Nov 22 at 8:51
francescop21
1,004115
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Provided $-1le xle 1$, you get:
begin{align}
left|x sqrt{1-x^2} +x right| = sqrt{1+x^2}\
left|x left(sqrt{1-x^2} +1right) right| = sqrt{1+x^2}\
|x|left(sqrt{1-x^2} +1right) = sqrt{1+x^2}\
x^2left(sqrt{1-x^2} +1right)^2 = 1+x^2\
x^2left(1-x^2+2sqrt{1-x^2}+1right) = 1+x^2\
2x^2sqrt{1-x^2}=x^4-x^2+1\
4x^4left(1-x^2right)=left(x^4-x^2+1right)^2
end{align}
answered Nov 22 at 8:51
francescop21
1,004115
add a comment |
up vote
0
down vote
accepted
Provided $-1le xle 1$, you get:
begin{align}
left|x sqrt{1-x^2} +x right| = sqrt{1+x^2}\
left|x left(sqrt{1-x^2} +1right) right| = sqrt{1+x^2}\
|x|left(sqrt{1-x^2} +1right) = sqrt{1+x^2}\
x^2left(sqrt{1-x^2} +1right)^2 = 1+x^2\
x^2left(1-x^2+2sqrt{1-x^2}+1right) = 1+x^2\
2x^2sqrt{1-x^2}=x^4-x^2+1\
4x^4left(1-x^2right)=left(x^4-x^2+1right)^2
end{align}
answered Nov 22 at 8:51
francescop21
1,004115
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Provided $-1le xle 1$, you get:
begin{align}
left|x sqrt{1-x^2} +x right| = sqrt{1+x^2}\
left|x left(sqrt{1-x^2} +1right) right| = sqrt{1+x^2}\
|x|left(sqrt{1-x^2} +1right) = sqrt{1+x^2}\
x^2left(sqrt{1-x^2} +1right)^2 = 1+x^2\
x^2left(1-x^2+2sqrt{1-x^2}+1right) = 1+x^2\
2x^2sqrt{1-x^2}=x^4-x^2+1\
4x^4left(1-x^2right)=left(x^4-x^2+1right)^2
end{align}
answered Nov 22 at 8:51
francescop21
1,004115
Provided $-1le xle 1$, you get:
begin{align}
left|x sqrt{1-x^2} +x right| = sqrt{1+x^2}\
left|x left(sqrt{1-x^2} +1right) right| = sqrt{1+x^2}\
|x|left(sqrt{1-x^2} +1right) = sqrt{1+x^2}\
x^2left(sqrt{1-x^2} +1right)^2 = 1+x^2\
x^2left(1-x^2+2sqrt{1-x^2}+1right) = 1+x^2\
2x^2sqrt{1-x^2}=x^4-x^2+1\
4x^4left(1-x^2right)=left(x^4-x^2+1right)^2
end{align}
answered Nov 22 at 8:51
francescop21
1,004115
answered Nov 22 at 8:51
francescop21
1,004115
answered Nov 22 at 8:51
francescop21
1,004115
answered Nov 22 at 8:51
francescop21
1,004115
1,004115
add a comment |
add a comment |
Amr Samir is a new contributor. Be nice, and check out our Code of Conduct.
Amr Samir is a new contributor. Be nice, and check out our Code of Conduct.
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1
Use LaTeX to write
– ramanujan
Nov 21 at 12:01