Prove that `|a a x m m m b x b|=m(x-a)(x-b)`

Prove that |{:(a, a, x), (m, m, m), (b, x, b):}|=m(x-a)(x-b)

Prove that abs((a,a,x),(m,m,m),(b,x,b))=m(x-a)(x-b)

If |a a x m m m b x b|=0,\ then x may be equal to- a. a b. b c. a+b d. m

If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^(n) , Prove that : a^(m-n) . b^(n - 1) . c^(l-m) = 1

If by eliminating x between the equations x^2 + ax + b = 0 and xy + l(x + y) + m = 0 , a quadratic in y is formed whose roots are the same as those of the original quadratic in x, then prove that either a = 2l and b = m or b + m = al

If y=(x-a)^(m)(x-b)^(n) , prove that (dy)/(dx)=(x-a)^(m-1)(x-b)^(n-1)[(m+n)x-(an+bm) ].

Integration OF ( dx/ a+b sinx & dx / a+b cosx) || Integration OF [ ( dx/ Sin^m x Cos^m x )OR ( dx/ (x-a)^m(x-b)^n ) ]

The value of 'c' in Lagrange's mean value theorem for f(x) = ( x - a)m (x - b)^(m) [a, b]^(n) is [a,b] is

Prove that the straight lines (x)/(a)-(y)/(b)=m and (x)/(a)+(y)/(b)=(1)/(m), where a and b are 'm' is a parameter,always meet on agiven positive real numbers and hyperbola.