Let and be two real roots of the equation ( k +1) ^2 x- 2 x=(1- k ) where k ( -1) and are real numbers. If ^2( + )=50 , then a value of is

Step-by-step solution

Given equation is aligned & ( k +1) ^2 x- 2 x=(1- k ) (i) & ( k +1) ^2 x- 2 x+( k -1)=0 (ii) aligned and are two real roots. aligned & + = 2 k+1 & = k-1 k+1 aligned Now, ( + )= + 1- aligned & = 2 k +1 1- ( k -1) k +1 & = 2 2 aligned aligned & ( + )= 2 & ^2( + )= ^2 2 & 50= ^2 2 & ^2=100 & =10 aligned