线性代数网课代修|ENGO361代写|ENGO361英文辅导|ENGO361

如果你也在线性代数linearalgebra这个学科遇到相关的难题,请随时添加vx号联系我们的代写客服。我们会为你提供专业的服务。 linearalgebra™长期致力于留学生网课服务,涵盖各个网络学科课程:金融学Finance,经济学Economics,数学Mathematics,会计Accounting,文学Literature,艺术Arts等等。除了网课全程托管外,linearalgebra™也可接受单独网课任务。无论遇到了什么网课困难,都能帮你完美解决! Use the sum and product properties to write a quadratic equation whose solutions are the following: 1. \(-6,\dfrac{1}{4}\). 2. \(\dfrac{1+\sqrt{13}}{2},\dfrac{1-\sqrt{13}}{2}\). 17. If \(a\) and \(b\) are the solutions to the equation \(x^{2}-5x+9=0\), then what is the value of \((a-1)(b-1)\)? 18. Given that \(m^{2}+71m-1990=0\), \(n^{2}+71n-1999=0\), and \(m\neq n\), find the value of \[\dfrac{1}{m}+\dfrac{1}{n}.\] 19. If \(a\) and \(b\) are two distinct real numbers that satisfy \(a^{2}=4a+3\) and \(b^{2}=4b+3\), find the value of \(\dfrac{b^{2}}{a}+\dfrac{a^{2}}{b}\). 20. For what integer \(a\) are both roots of \(x^{2}+ax+17=0\) positive integers? 21. Let \(x_{1}\) and \(x_{2}\) be the solutions of \(2x^{2}+5x+3=0\). Find 1. \(x_{1}^{2}+x_{2}^{2}\), 2. \(\dfrac{x_{2}}{x_{1}}+\dfrac{x_{1}}{x_{2}}\), 3. \((x_{1}-2)(x_{2}-2)\), 4. \((x_{1}-x_{2})^{2}\).22. Given that \(x^{2}-3x-4=0(*)\), write an equation whose solutions are 1. the opposites of the solutions of \((*)\). 2. the reciprocals of the solutions of \((*)\). 3. one more than the solutions of \((*)\). 4. the cubes of the solutions of \((*)\). 23. Suppose that the equation \(7x^{3}-ax^{2}+bx-12=0\) has three real, positive roots \(r_{1}\), \(r_{2}\) and \(r_{3}\). If \[\frac{7r_{1}}{2}+\frac{r_{2}}{3}+\frac{r_{3}}{2}=3,\] find the values of \(a\) and \(b\). 24. Find the roots \(r_{1}\), \(r_{2}\), \(r_{3}\) and \(r_{4}\) of the equation \(4x^{4}-ax^{3}+bx^{2}-cx+5=0\), knowing they are real, positive and that \[\frac{r_{1}}{2}+\frac{r_{2}}{4}+\frac{r_{3}}{5}+\frac{r_{4}}{8}=1.\] Find \(a\), \(b\) and \(c\) as well. 25. Find all real numbers \((a,b,c,d)\) such that \[a+bcd = 2\] \[b+cda = 2\] \[c+dab = 2\] \[d+abc = 2.\]**1.7Evaluating Algebraic Expressions****Definitions**1. An _algebraic expression_ is a collection of numbers, variables, operations, and grouping symbols. When each variable in an algebraic expression is replaced by a number, we say that we are _evaluating_ the expression, and the resulting number is the _value of the expression_. **2. Find the value of \[\frac{x^{4}-6x^{3}-2x^{2}+18x+23}{x^{2}-8x+15}\] where \(x=4-\sqrt{3}\). 3. Find the numerical value of \(2a^{2}-5a-2+\frac{3}{1+a^{2}}\), if \(a^{2}-3a+1=0\). 4. Given that \(x=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}\) and \(y=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\), evaluate the expression \[\frac{2\sqrt{10(x+y)}-3\sqrt{xy}}{3x^{2}-5xy+3y^{2}}.\] 5. If \(\frac{x}{x^{2}+x+1}=a\), (\(a\neq\frac{1}{2}\)), then express \(\frac{x^{2}}{x^{4}+x^{2}+1}\) in terms of \(a\). 6. Evaluate \[\frac{a}{bc}+\frac{b}{ca}+\frac{c}{ab}-\frac{1}{a}-\frac{1}{b}-\frac{1}{c}\] if \(a+x^{2}=2006\), \(b+x^{2}=2007\), \(c+x^{2}=2008\), and \(abc=24\). 7. Find the value of \[\frac{\left(\frac{1}{a}+\frac{1}{b}\right)^{3}}{\left(\frac{1}{a}-\frac{1}{b} \right)^{2}}\] where real numbers \(a\) and \(b\) satisfy \(4a^{2}-4a+1+\sqrt{1-ab}=0\). 8. Find the numerical value of \[\frac{x+\sqrt{xy}-y}{2x+\sqrt{xy}+3y}\] given that \(\sqrt{x}(\sqrt{x}+2\sqrt{y})=\sqrt{y}(6\sqrt{x}+5\sqrt{y})\), where \(x>0\) and \(y>0\). 9. If \(a\), \(b\), and \(c\) are nonzero real numbers such that \[\frac{a+b-c}{c}=\frac{a-b+c}{b}=\frac{-a+b+c}{a},\] find all possible values of \(\frac{(a+b)(b+c)(c+a)}{abc}\).10. Find \(x^{6}+\frac{1}{x^{6}}\), if \(x+\frac{1}{x}=3\). 11. Find all possible values of \(ab\) given that \(a+b=2\) and \(a^{4}+b^{4}=16\). **The Problems!** 12. Evaluate \(\frac{2a+b-c}{a-b+c}\), if \(\frac{a}{2}=\frac{b}{4}=\frac{c}{5}\neq 0\). 13. Given that \(\frac{1}{a}-\frac{1}{b}=4\), find \(\frac{a-2ab-b}{2a+7ab-2b}\). 14. If \(|ab+2|+|a+1|=0\), compute \[\frac{1}{(a-1)(b+1)}+\frac{1}{(a-2)(b+2)}+\cdots+\frac{1}{(a-2009)(b+2009)}.\] 15. Find the value of \(\frac{x^{4}-4x^{3}-x^{2}+9x-4}{x^{2}-4x+5}\), given that \(x=2-\sqrt{3}\). 16. Evaluate \((4x^{3}-1997x-1994)^{2009}\) if \(x=\frac{1+\sqrt{1994}}{2}\). 17. Find the value of \(a^{2}+b^{2}+c^{2}\) given that the real numbers \(a\), \(b\), and \(c\) satisfy \(a+b+c=-1\) and \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\). 18. If \(x-\frac{1}{x}=2\), find \(x^{3}-\frac{1}{x^{3}}+\frac{2}{x}-2x\). 19. Evaluate \(x^{4}+y^{4}+(x+y)^{4}\), if \(x=\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}\) and \(y=\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}\). 20. If \(x+y=4\) and \(xy=2\), find \(x^{6}+y^{6}\). 21. Find all possible values of \(x^{3}+\frac{1}{x^{3}}\), given that \(x^{2}+\frac{1}{x^{2}}=7\). 22. If real numbers \(a\), \(b\), \(c\), and \(d\) satisfy \(a+b+c+d=20\) and \(ac+ab+ad+bc+bd+cd=150\), prove that they are all equal图片描述

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