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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

A

`45^(@)`

B

`35^(@)`

C

`120^(@)`

D

`30^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given that , `2a^(2)b^(2)+2b^(2)c^(2)=a^(4)+b^(4)+c^(4)`
`rArra^(4)+b^(4)+c^(4)-2a^(2)b^(2)-2b^(2)c^(2)+2a^(2)c^(2)=2a^(2)c^(2)`
`rArr(a^(2)-b^(2)+c^(2))^(2)=2c^(2)a^(2)`
`rArr(a^(2)-b^(2)+c^(2))/(2ca)=+-(1)/(sqrt(2))=cosB`
`rArrcosB=cos45^(@)orcos135^(@)`
`rArrB=45^(@)or135^(@)`
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