Question

√x2 + 1 + √x2 – 2x + 3 = 3

│ x-4 │ - │ 2–0,5x│ ≤ 3

│5- x2-6 │= x2-5x-6

x2-2x+3 : x2-4x+3 > -2


Could I get help with solving these please?

Answer 1

You probably got no reply so far since your equations are not clearly stated.

e.g. in the first one, do you mean
√(x^2+1) + √(x^2-2x3+3) = 3 ?

(the way you have it typed, I could simplify it to 2√(x^2) - 2x + 1 = 0 )

If I assumed √(x^2+1) + √(x^2-2x3+3) = 3
then √(x^2-2x3+3) = 3 - √(x^2+1)
square both sides and simplify to get
6√(x^2 + 1) = 7 + 2x

square again, and solve using the quadratic equation formula.
I got x = (28 ±√2448)/64 or
x = approx. 1.21058 or -.3356
(both answers verified in my equation)

for the second, the part shown as │2 - 0,5x│ has me confused

in the third, is the first part not simply │-1 - x^2│ ?

In the last is it
(x2-2x+3) ÷ (x2-4x+3) > -2 ?
which would be
(x2-2x+3) / (x2-4x+3) > -2

Please re-type your equations.