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

(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^2b^2=2c^2(a^2+b^2) ,, then show that angleC=60^@or120^@

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-

Factorise : a^(4)(b^(2)-c^(2))+b^(4)(c^(2)-a^(2))+c^(4)(a^(2)-b^(2))

If (b^(2)+c^(2)-a^(2))/(2bc), (c^(2)+a^(2)-b^(2))/(2ca) and (a^(2)+b^(2)-c^(2))/(2ab) are in A.P. then show that, a(b+c-a), b(c+a-c) and c(a+b-c) are also in A.P. [a+b+c != 0] .

Factorise : 2b^(2)c^(2)+2c^(2)a^(2)+2a^(2)b^(2)-a^(4)-b^(4)-c^(4)

If (5a-3b)/a= (4a+b-2c)/(a+4b-2c) = (a+2b-3c)/(4a-4c) , then show that 6a=4b=3c.

If c^(2) = a^(2) + b^(2) , then prove that 4s (s - a) (s - b) (s - c) = a^(2) b^(2)

Prove that {:|( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) |:} =4a^(2) b^(2) c^(2)

Show that the length of the common chord of the circles (x-a)^(2) + (y-b)^(2) = c^(2) and (x-b)^(2) + (y-a)^(2) = c^(2) is sqrt(4c^(2) -2(a-b)^(2)) unit.