If the function f(x)= array l 2 x (k₁+1 ) x+ (k₂-1 ) x , x 0 4, x=0 2 x _e ( 2+k₁ x 2+k₂ x ), x 0 array . is continuous at x =0 , then k ₁^2+ k ₂^2 is equal to

Step-by-step solution

aligned & _ x 0⁻ 2 x ( k ₁+1 ) x + ( k ₂-1 ) x =4 & 2 ( k ₁+1 )+2 ( k ₂-1 )=4 & k ₁+ k ₂=2 & _ x 0⁺ 2 x ( 2+ k ₁ x 2+ k ₂ x )=4 & _ x 0⁺ 1 x (1+ ( k ₁- k ₂ ) x 2+ k ₂ x )=2 & k ₁- k ₂ 2 =2 & k ₁- k ₂=4 & k ₁=3, k ₂=-1 & k ₁^2+ k ₂^2=9+1=10 aligned