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what 2 numbers add to get 7 and multiply to get 2

 Feb 13, 2019
 #1
avatar+18324 
+1

x *y = 2

x+y=7     y = 7-x    sub this into the first equation

 

x*(7-x) = 2

7x - x^2 -2 = 0

x^2-7x+2 = 0           Qudratic formula   a = 1 b = -7  c = 2       { 7+- sqrt ( 49-8)} /2      x = 3.5 +- sqrt(10.25)=   6.702   and  .2984

 Feb 13, 2019
 #2
avatar+7499 
+2

Let a and b be those 2 numbers.

 

\(\begin{cases}a+b=7\\ab=2\end{cases}\\ a + \dfrac{2}{a} = 7\\ a^2 -7a + 2 = 0\\ a = \dfrac{7 \pm \sqrt{45}}{2}\\ a = \dfrac{7 +3\sqrt5}{2} \text{ OR }a = \dfrac{7-3\sqrt5}{2}\\ \text{When }a = \dfrac{7+3\sqrt5}{2},b=\dfrac{7-3\sqrt5}{2}\\ \text{When }a = \dfrac{7-3\sqrt5}{2},b=\dfrac{7+3\sqrt5}{2}\\ \text{The solutions are }(a,b) = \left(\dfrac{7-3\sqrt5}{2},\dfrac{7+3\sqrt5}{2}\right)\text{ or }(a,b) = \left(\dfrac{7+3\sqrt5}{2},\dfrac{7-3\sqrt5}{2}\right)\)

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 Feb 14, 2019

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