bbb911
Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Solve.

[tex] \sqrt{x-1}+3=x [/tex]

Sagot :

[tex]\sqrt{x-1}+3=x;\ Domain:x-1\geq0\ \wedge\ x\geq3\to x\geq1\ \wedge\ x\geq3\\D:x\in[3;\ \infty)\\\\\sqrt{x-1}=x-3\ \ \ \ |square\ both\ sides\\\\x-1=(x-3)^2\ \ \ \ |use\ of\ the\ formula:(a-b)^2=a^2-2ab+b^2\\\\x-1=x^2-6x+9\\\\x^2-6x+9=x-1\\\\x^2-6x-x+9+1=0\\x^2-7x+10=0\ \ \ \ |use\ quadratic\ formula[/tex]

[tex]a=1;\ b=-7;\ c=10\\\\\Delta=b^2-4ac\to\Delta=(-7)^2-4\cdot1\cdot10=49-40=9\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt9=3\\\\x_1=\frac{7-3}{2\cdot1}=\frac{4}{2}=2\notin D\\\\x_2=\frac{7+3}{2\cdot1}=\frac{10}{2}=5\in D\\\\Solution:x=5[/tex]
konrad509
[tex]\sqrt{x-1}+3=x\\ \sqrt{x-1}=x-3\\ D:x-1\geq0 \wedge x-3\geq0\\ D:x\geq1 \wedge x\geq3\\ D:x\geq3\\ x-1=(x-3)^2\\ x-1=x^2-6x+9\\ x^2-7x+10=0\\ x^2-2x-5x+10=0\\ x(x-2)-5(x-2)=0\\ (x-5)(x-2)=0\\ x=5 \vee x=2\\ 2\not \in D \Rightarrow x=5[/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.