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In triangle, A B Cif2a^2b^2+2b^2c^2=a^2+...

In triangle, `A B Cif2a^2b^2+2b^2c^2=a^2+b^4+c^4,` then angle B is equal to `45^0` (b) `135^0` `120^0` (d) `60^0`

A

`45^(@)`

B

`135^(@)`

C

`120^(@)`

D

`60^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`2a^(2)b^(2) + 2b^(2)c^(2) = a^(4) + b^(4) + c^(4)`
Also, `(a^(2) -b^(2) + c^(2)) = a^(4) + b^(4) + c^(4) - 2(a^(2) b^(2) + b^(2) c^(2) - c^(2) a^(2))`
`:. (a^(2) -b^(2) + c^(2))^(2) = 2c^(2) a^(2)`
`:. (a^(2) -b^(2) + c^(2))/(2ca) = +- (1)/(sqrt2) = cosB`
or `B = 45^(@) or 135^(@)`
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