Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Remember:
[tex](\sqrt[n]{a})^n=a\\\\(a+b)=a^2+2ab+b^2[/tex]
Given the equation [tex]\sqrt{17-x}=x+3[/tex], you need to solve for the variable "x" to find its value.
You need to square both sides of the equation:
[tex](\sqrt{17-x})^2=(x+3)^2[/tex]
[tex]17-x=(x+3)^2[/tex]
Simplifying, you get:
[tex]17-x=x^2+2(x)(3)+3^2\\\\17-x=x^2+6x+9\\\\x^2+6x+9+x-17=0\\\\x^2+7x-8=0[/tex]
Factor the quadratic equation. Find two numbers whose sum be 7 and whose product be -8. These are: -1 and 8:
[tex](x-1)(x+8)=0[/tex]
Then:
[tex]x_1=1\\x_2=-8[/tex]
Let's check if the first solution is correct:
[tex]\sqrt{17-(1)}=(1)+3[/tex]
[tex]4=4[/tex] (It checks)
Let's check if the second solution is correct:
[tex]\sqrt{17-(-8)}=(-8)+3[/tex]
[tex]5\neq-5[/tex] (It does not checks)
Therefore, the solution is:
[tex]x=1[/tex]
