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In triangle ABC if a^(4) + b^(4) + c^(4)...

In triangle ABC if `a^(4) + b^(4) + c^(4) = 2a^(2)b^(2) + 2b^(2)c^(2)` then the values of B will be-

A

`45^(@)`

B

`135^(@)`

C

`120^(@)`

D

`60^(@)`

Text Solution

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The correct Answer is:
A, B
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Explore conceptually related problems

(i) If in a triangle ABC, a^(4) + b^(4) +c^(4) - 2b^(2) c^(2) -2c^(2)a^(2)=0 , then show that, C=45^(@) or 135^(@) . (ii) In in a triangle ABC, sin^(4)A + sin^(4)B + sin^(4)C = sin^(2)B sin^(2)C + 2sin^(2) C sin^(2)A + 2sin^(2)A sin^(2)B , show that, one of the angles of the triangle is 30^(@) or 150^(@)

If a^(4) + b^(4) + c^(4) + a^(2)b^(2) = 2c^(2)(a^(2) + b^(2)) then show that, C=60^(@) or 120^(@)

Knowledge Check

  • If a, b, c are the sides of the triangle ABC such that a^(4) +b^(4) +c^(4)=2x^(2) (a^(2)+b^(2)), then the angle opposite to the side c is-

    A
    `45^(@) or 135^(@)`
    B
    `30^(@) or 120^(@)`
    C
    `60^(@) or 150^(@)`
    D
    none of these

  • If a^2+b^2+c^2=2(a-b-c)-3 then the value of (2a-3b+4c) will be

    A
    0
    B
    -1
    C
    1
    D
    2

  • In triangle ABC, if a^(2) + b^(2) +c^(2) -bc -ca -ab=0, then the value of sin ^(2)A+ sin ^(2)B+sin ^(2)C is -

    A
    `9/4`
    B
    `4/9`
    C
    `(3sqrt3)/(2)`
    D
    `3/2`

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