Question

( √5-2)х-1/х+1≤( √5+2)х-1

Answer 1

Х>=0

вроде так, решал системой 

Answer 2

корень(5-2)х сокращается, остается

-1/х+1≤ -1

-1/х≤-1-1

-1/х ≤-2

х здесь вроде знак меньше или равно меняется наоборот -1/-2

х больше или равно 0,5

Вроде так, словами пишу, не охота знак искать

 при проверке если х вставить получается

Answer 3

To solve the inequality, we can start by simplifying the expression on the left-hand side:

(√5-2)х-1/х+1 = ((√5-2)х-1)/(х+1)

Then, we can multiply both sides by (x+1) to get rid of the denominator on the left-hand side:

((√5-2)х-1)/(х+1) * (x+1) ≤ (√5+2)х-1 * (x+1)

Simplifying the right-hand side, we get:

(√5+2)х-1 * (x+1) = (√5+2)х-1 * x + (√5+2)х-1

Now, we can simplify the left-hand side by multiplying out the numerator:

((√5-2)х-1) * (x+1) = (√5-2)х + (√5-2)х-1

Substituting these simplified expressions back into the inequality, we get:

(√5-2)х + (√5-2)х-1 ≤ (√5+2)х-1 * x + (√5+2)х-1

We can simplify this further by moving all the x terms to one side and all the constant terms to the other side:

(√5-2)х - (√5+2)х-1 * x ≤ (√5+2)х-1 - (√5-2)х-1

Now, we can factor out x from the left-hand side:

x((√5-2) - (√5+2)х-2) ≤ (√5+2)х-1 - (√5-2)х-1

Simplifying the expressions in parentheses, we get:

x(-4/((√5+2)(√5-2))) ≤ 4/((√5+2)(√5-2))

Multiplying both sides by -1, we get:

x(4/((√5+2)(√5-2))) ≥ -4/((√5+2)(√5-2))

Finally, we can divide both sides by 4/((√5+2)(√5-2)) to isolate x:

x ≥ -1/((√5+2)(√5-2)/4)

Simplifying the expression in the denominator, we get:

x ≥ -1/(3+√5)

Therefore, the solution to the inequality is:

x ≥ -1/(3+√5)