Question

1) 2root(5-2X)-2root(X+17)=0
2) X^2-2-(X^2+8)/(X^2+2)=0
3) 2/(X^2-X-12)+6/(X^2+4X+3)=1/(X+3)

Answer 1

1)ОДЗ 5-2x≥0⇒x≤2,5 U x+17≥0⇒x≥-17
x∈[-17;2,5]
2√(5-2x)=2√(x+17)
5-2x=x+17
x+2x=5-17
3x=-12
x=-4
2)x²-2=(x²+8)/(x²+2)
x^4-4-x²-8=0
x^4-x^2-12=0
x²=a
a²-a-12=0
a1+a2=1 U a1*a2=-12
a1=-3⇒x²=-3 нет решения
a2=4⇒x²=4⇒x=+-2
3)2/(x-4)(x+3) +6/(x+1)(x+3)=1/(x+3)
x≠4  x≠-3    x≠-1
2(x+1)+6(x-4)=(x+1)(x-4)
x²-4x+x-4-2x-2-6x+24=0
x²-11x+18=0
x1+x2=11 U x1*x2=18
x1=2  x2=9