Răspuns:
Buna!
1.[tex]\sqrt{x+1} =2[/tex]
=x+1=4
x=4-1=3
[tex]\sqrt{3+1}[/tex]=2
Simplificam 2=2,deci x=3
2. [tex]\sqrt{x-13}[/tex]=1
x-13=1
x=1+13
x=14
[tex]\sqrt{14-13}[/tex]=1
1=1,deci x=14
3.
Ecuatia vand doua solutii: x=-2 sau 3
[tex]\sqrt{x^{2} } -x-2=2\\x^{2}-x-2=4\\x^{2} -x-2-4=0\\x^{2}+2x-3x-2-4=0\\x^{2} +2x-3x-6=0\\x*(x+2)-3x-6=0\\x*(x+2)-3(x+2)=0\\(x+2)*(x-3)=0\\x+2=0\\x-3=0\\deci.x=-2 , x-3=0\\adica. x=-2 , x=3\\[/tex]
4.
[tex]\sqrt{x^{2}-x-2= } (x-2)\\x^{2} -x-2-x^{2} -4x+4\\-x-2=-4x+4\\-x+4x-2=4\\-x+4x=4+2\\3x=4+2\\3x=6[/tex]acum impartim ambele parti ale ecuatiei la 3:
x=2
5.
[tex]\sqrt[3]{8x^{3}+x-2= } 2x\\[/tex]
Ridicam ambele parti ale ecuatiei la puterea 3:
[tex]8x^{3} +x-2=8x^3\\x-2=0\\x=2[/tex]
Dupa cum se observa,aici am eliminat terenii egali din ambele parti ale ecuatiei,rezultand solutia : x=2
6. [tex]\sqrt{x} +8-\sqrt{x} =2[/tex]
Vom muta expresia si vom schimba semnul:[tex]\sqrt{x} +8=2+\sqrt{x}[/tex]
=[tex]x+8=4+4\sqrt{x} +x\\8=4+4\sqrt{x} \\-4\sqrt{x} +8=4\\-4\sqrt{x} =4-8\\-4\sqrt{x} =-4\\\sqrt{x} =1\\x=1[/tex]
