Lagrangian: Maximizing Output from CES Production Function with Cost Constraint

I don't understand the part where you got L=1/25k
It's like you did magic
L is supposed to be 2.5k or 5k

you beautiful man

Are we multiplying by 5 because it’s the reciprocal of 1/5?

you rescued me from my math in econ exam. Thank you so much

Why -2 Raised?sir

CES stands for

If the firm chose 50 L and 250 K, wouldn't the output be bigger at same costs (1'000)?

You really helped me I was stuck
Thankyou

how did you get -2 that you raise/ multiplied

How did you get the -2 which raise to the power of both sides?

Both output maximization and cost minimization leads to same input combination?

What does the lambda mean tho? I dont really get it. Please help me explain..

Thank you, greeting from Colombia.