Question

Buna ziua,ma poate ajuta cineva la ex acestea??? Va rog

Answer 1

Răspuns:

Buna!

1.$\sqrt{x+1} =2$

=x+1=4

x=4-1=3

$\sqrt{3+1}$=2

Simplificam 2=2,deci x=3

2. $\sqrt{x-13}$=1

x-13=1

x=1+13

x=14

$\sqrt{14-13}$=1

1=1,deci x=14

3.

Ecuatia vand doua solutii: x=-2 sau 3

$\sqrt{x^{2} } -x-2=2\\x^{2}-x-2=4\\x^{2} -x-2-4=0\\x^{2}+2x-3x-2-4=0\\x^{2} +2x-3x-6=0\\x*(x+2)-3x-6=0\\x*(x+2)-3(x+2)=0\\(x+2)*(x-3)=0\\x+2=0\\x-3=0\\deci.x=-2 , x-3=0\\adica. x=-2 , x=3$

4.

$\sqrt{x^{2}-x-2= } (x-2)\\x^{2} -x-2-x^{2} -4x+4\\-x-2=-4x+4\\-x+4x-2=4\\-x+4x=4+2\\3x=4+2\\3x=6$acum impartim  ambele parti ale ecuatiei la 3:

x=2

5.

$\sqrt[3]{8x^{3}+x-2= } 2x$

Ridicam ambele parti ale ecuatiei la puterea 3:

$8x^{3} +x-2=8x^3\\x-2=0\\x=2$

Dupa cum se observa,aici am eliminat terenii egali din ambele parti ale ecuatiei,rezultand solutia : x=2

6. $\sqrt{x} +8-\sqrt{x} =2$

Vom muta expresia si vom schimba semnul:$\sqrt{x} +8=2+\sqrt{x}$

=$x+8=4+4\sqrt{x} +x\\8=4+4\sqrt{x} \\-4\sqrt{x} +8=4\\-4\sqrt{x} =4-8\\-4\sqrt{x} =-4\\\sqrt{x} =1\\x=1$