how to simplify and solve this equation :
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.
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.
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.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3007626%2fhow-to-simplify-and-solve-this-equation%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
Use LaTeX to write
– ramanujan
Nov 21 at 12:01