যদি (x + y) ^((1)/(3)) + (y + x) ^(1)/(3)) =- (z + x ) ^((1)/(3)) , তারপর (x ^(3) + y ^(3) + z...

If (x + y) ^((1)/(3)) + (y + x) ^((1)/(3)) =- ( z + x ) ^((1)/(3)) , then (x ^(3) + y ^(3) + z ^(3)) can be expressed as :

(x + y) ^ (3) + (y + z) ^ (3) + (z + x) ^ (3) -3 (x + y) (y + z) (z + x)

Find the S.D. between the lines : (i) (x)/(2) = (y)/(-3) = (z)/(1) and (x -2)/(3) = (y - 1)/(-5) = (z + 4)/(2) (ii) (x -1)/(2) = (y - 2)/(3) = (z - 3)/(2) and (x + 1)/(3) = (y - 1)/(2) = (z - 1)/(5) (iii) (x + 1)/(7) = (y + 1)/(-6) = (z + 1)/(1) and (x -3)/(1) = (y -5)/(-2) = (z - 7)/(1) (iv) (x - 3)/(3) = (y - 8)/(-1) = (z-3)/(1) and (x + 3)/(-3) = (y +7)/(2) = (z -6)/(4) .

If x^((1)/(3))+y^((1)/(3))+z^((1)/(3))=0;x+y+z=

Find (x+y+z)^(3)-(x+y-z)^(3)-(y+z-x)^(3) -(z + x-y)^(3)