" The curve "x+y-ln(x+y)=2x+5" has a vertical tangent at the point "(alpha,beta)." Then "alpha+beta" is equal to "

The curve x+y-log_(e)(x+y)=2x+5 has a vertical tangent at the point (alpha, beta). then alpha+beta is equal to

If the point on the curve y ^(2) = 6x, nearest to the point ( 3, (3)/(2)) is ( alpha, beta) then 2 ( alpha + beta) is equal to _________.

The graph of 2x=5-3y cuts the x-axis at the point P(alpha,beta) . The value of (2alpha+beta) is :

The graph of 2x = 5-3y cuts the x-axis at the point P( alpha,beta ). The value of (2alpha+beta) is

If f(x) = 5 log_(5)x then f^(-1)(alpha - beta) where alpha , beta in R is equal to

If y=e^x+e^-x+2 has a tangent parallel to x-axis at (alpha,beta) then find the value of alpha .

If the polynomial x^2+3x+5 has roots alpha and beta then alpha/beta+beta/alpha

If the tangent drawn to the curve y=x^(3)+3x^(2)+2x+2" at "(0,2) also touches the curve y=kx^(2) at (alpha,beta), then absolute value of (alpha+(beta)/(k)) equal to

If the chord joining the points where x=p, x=q on the curve y=ax^(2)+bx+c is parallel to the tangent to the curve (alpha, beta)( then alpha=