The roots of the equation `l^(2)(m^(2)-n^(2))x^(2)+m^(2)(n^(2)-l^(2))x+n^(2)(I^(2)-m^(2))=0` are

Factoris the expression. l ^(2) m ^(2) n - lm ^(2) n ^(2) - l^(2) mn ^(2)

The square root of x^(m^(2) - n^(2)).x^(n^(2) + 2mn).x^(n^(2)) is

sqrt(m^(2)n^(2))times root(6)(m^(2)n^(2))times root(3)(m^(2)n^(2))

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

Find the squre root of (m^(n^(2)) n^(m^(2)) a^((m +n)))/((m + n)^((m +n)^(2)))

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If l_(1)=1/sqrt(3), m_(1)=1/sqrt(3) then the value of n_(1) is equal to

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) The angle between the lines whose direction cosines are (1/2, 1/2,1/sqrt(2)) and (-1/2, -1/2, 1/sqrt(2)) is

Write the greatest common factor in each of the term. l ^(2) m ^(2) n, l m ^(2) n ^(2) , l ^(2) mn ^(2)

If two roots of the equation x^(3)+mx^(2)+11x-n=0 are 2 and 3 then (m+n)=

If (l_(1), m_(1), n_(1)) , (l_(2), m_(2), n_(2)) are D.C's of two lines, then (l_(1)m_(2)-l_(2)m_(1))^2+(m_(1)n_(2)-n_(1)m_(2))^2+(n_(1)l_(2)-n_(2)l_(1))^2+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^2=