a + b + c

In the triangle ABC , If ( a + b + c )(a + b - c) = k ab

Prove that : k $\in \left( 0,2 \right) \quad ,\quad then\quad find\quad m\quad \left( \angle c \right) \quad when\quad k=1\quad$

#Geometry #Angles #Trigonometry #Triangle #Cosine

Easy Math Editor

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Comments

If ( a + b + c )(a + b - c) = kab then a²+b² -c²=(k-2)ab and thus cos(C)=(a²+b² -c²)/(2ab) =(k-2)/2 and -1≤cos(C)≤0 or -1≤(k-2)/2≤0 or 0≤(k≤2. Further if k=1 then cos(C)=(k-2)/2= (1-2)/2=-1/2 or C=120°.

Ajit Athle - 5 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$