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Grade 11Algebra

In a triangle ABC, if a4-2(b2+c2)a2+b4+b2c2+c4=0, then angle A is 60° or 120°. Is it true!?

Profile image of Aman Sirohi
7 Years agoGrade 11
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1 Answer

Profile image of Arun
7 Years ago
 
=a4+b4+c4=2c2(a2+b2)
=a+b+c-2ac-2bc=0
add 2ab on both sides,we get
=a+b+c+2ab-2bc-2ca=2ab,
=(a+b-c)=2ab
multiply and divide with 2 on RHS of the equation.we get \frac{(a^{2}+b^{2}-c^{2})^{2}}{4b^{2}c^{2}}
=\frac{1}{2},
we know that cosC=\frac{a^{2}+b^{2}-c^{2}}{2bc},
cos2C=\frac{1}{2}
cosC=\frac{1}{\sqrt{2}},
we get C=\frac{\pi }{4} or \frac{3\pi }{4}

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