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# A lot of questions:

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Hi guys,

I have a lot of questions to ask and anyone answering doesn't need to post every answer in one long post!! TYSM

1. Let $a$ and $b$ be the solutions to $5x^2-11x+4=0$. Find $$1/a+1/b$$

2.Let $u$ and $v$ be the solutions to $3x^2+5x+7=0$. Find $$u/v+v/u$$

3.The roots of $7x^2+x-5=0$ and $a$ and $b$. Compute $(a-4)(b=4).$

4. The real numbers $x$ and $y$ are such that \begin{align*}
x + y &= 4, \\
x^2 + y^2 &= 22, \\
x^4 &= y^4 - 176 \sqrt{7}.
\end{align*}

Compute x-y.

5.The roots of $$x^2 + 5x + 3 = 0$$ are $p$ and $q$, and the roots of $$x^2 + bx + c = 0$$ are $p^2$ and $q^2$. Find $b$+$c$

May 21, 2021

#1
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the answer to a and b for one r {x=-(((sqrt(41)-11)/10)), x=((sqrt(41)+11)/10)}

May 21, 2021
#2
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just go to symbolab.com and plug them in

mathisopandcool  May 21, 2021
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1. By Vieta's formulas, 1/a + 1/b = 15/11.

May 22, 2021
#4
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2. u = -1/6*i*(sqrt(59) - 5i) and v = -1/6*i*(sqrt(59) + 5i), so u/v + v/u = ( -1/6*i*(sqrt(59) - 5i))/(-1/6*i*(sqrt(59) + 5i)) + (-1/6*i*(sqrt(59) + 5i))/ ( -1/6*i*(sqrt(59) - 5i)) = -8/19.

May 22, 2021