Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Answer: [tex]\begin{gathered} The\text{ value of x for the question:} \\ \text{x = -1.562 or x = 1.791} \end{gathered}[/tex]Explanation:[tex]\begin{gathered} Given: \\ \sqrt{5\text{ - x}}\text{ = 5 - x}^2 \\ We\text{ need to find the value of x} \end{gathered}[/tex]
To answer the question, we will solving and graphing to get the value of x
[tex]\begin{gathered} \sqrt{5\text{ - x}}\text{ = 5 - x}^2 \\ Square\text{ both sides:} \\ (\sqrt{5\text{ - x}})^2\text{ = \lparen5 - x}^2)^2 \\ 5\text{ - x = \lparen5 - x}^2)(5\text{ - x}^2)\text{ } \end{gathered}[/tex][tex]\begin{gathered} 5\text{ - x = 5\lparen5 - x}^2)\text{ - x}^2(5\text{ - x}^2) \\ 5\text{ - x = 25 - 5x}^2\text{ - 5x}^2\text{ + x}^4 \\ 5\text{ - x = 25 - 10x}^2\text{ + x}^4 \\ x^4\text{ - 10x}^2\text{ + x + 25 - 5 = 0} \\ x^4\text{ -10x}^2\text{ + x + 20 = = 0} \end{gathered}[/tex][tex]\begin{gathered} -x\text{ = x}^4\text{ - 10x}^2\text{ + 20} \\ \\ The\text{ highest degree in our expansion above is 4} \\ So\text{ to solve for x, we will represent x}^2\text{ with u} \\ \\ The\text{ expression becomes:} \\ u^2\text{ - 10u + 20 = -x} \\ u^2\text{ - 10 u + 20} \\ u\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ u\text{ = }\frac{-(-10)\pm\sqrt{(-10)^2-4(1)(20)}}{2(1)} \\ \text{ u = }\frac{10\pm\sqrt{100-80}}{2} \\ u\text{ = }\frac{10\pm2\sqrt{5}}{2}\text{ = }5\pm\sqrt{5} \\ u\text{ = 7.2361 or 2.7639} \end{gathered}[/tex][tex]\begin{gathered} NB:I\text{ couldn't proceed further because we have x in the expression after expansion.} \\ When\text{ the degree of the polynomial is to the 4th degree, and we want to solve algebraically,} \\ we\text{ need to have just 3 terms \lparen4th power, 2nd power and a constant\rparen to be able to represent } \\ \text{with a letter. }I\text{ n this case letter u} \end{gathered}[/tex][tex]\begin{gathered} left\text{ hand side will be equated to y} \\ and\text{ te right side equated to y} \\ Plotting\text{ both graphs on same coordinate} \\ The\text{ point of intersection of both graph will be the solution} \\ \\ From\text{ our graph:} \\ The\text{ point of intersection: }(-1.562,\text{ 2.562\rparen and \lparen1.791, 1.791\rparen} \end{gathered}[/tex][tex]\begin{gathered} The\text{ value of x for the question:} \\ \text{x = -1.562 or x = 1.791} \end{gathered}[/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.