Question

In a triangle ABC a²-c²=b(b-c)
√2a=2b-c and R=1/√3 Then find b​

Answer 1

Answer:

a

2

=b

2

+c

2

−2bccosA

b

2

=a

2

+c

2

−2accosB

c

2

=b

2

+a

2

−2bacosC

Adding above three equation and rearranging

2bccosA+2accosB+2abcosC=a

2

+b

2

+c

2

From the question

ac+

3

ab=a

2

+b

2

+c

2

⟹cosA=0,cosB=

2

1

,cosC=

2

3

So ∠A=90 degrees

So △ABC is right angles and not isoceles