Πέντε δύσκολες άρρητες εξισώσεις

 By Viet Dh 

Problem 1
Solve equation

  .

Solve:

Condition .

Equation has no root

.

We have

Problem 2
Solve equation

  .

Solve:

Condition .

We have

Setting

  .

Deduce

Thus

.

Problem 3
Solve equation

  .

Solve:

We have

Setting

.

Deduce

.

.

Setting . We obtain

Thus

.

Problem 4
Solve equation

  .

Solve:

Condition

 

Setting

 

We have

Thus

Setting . We obtain

Deduce

Problem 5
Solve equation

.

Solve:

Condition

.

We have

Setting

.

We obtain

Thus