Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 165876 by bounhome last updated on 09/Feb/22

solve: sin^2 x+sin^2 y+1=sinx+siny+sinxsiny

solve:sin2x+sin2y+1=sinx+siny+sinxsiny

Commented by MJS_new last updated on 10/Feb/22

u=sin x ∧v=sin y u^2 +v^2 +1=u+v+uv ⇔ v^2 −(u+1)v+u^2 −u+1=0 v∈R ⇔ −(3/4)(u−1)^2 ≥0 which is only possible with u=1 ⇒ v=−1 ⇒ sin x =1∧sin y =−1

u=sinx∧v=sinyu2+v2+1=u+v+uv⇔v2−(u+1)v+u2−u+1=0v∈R⇔−34(u−1)2⩾0whichisonlypossiblewithu=1⇒v=−1⇒sinx=1∧siny=−1

Commented by mindispower last updated on 10/Feb/22

u=1

u=1

Commented by MJS_new last updated on 10/Feb/22

yes.

yes.

Terms of Service

Privacy Policy

Contact: info@tinkutara.com