Question

# The sum of two numbers is 6, and the sum of their squares is 28. Find these numbers exactly

176

likes
879 views

## Answer to a math question The sum of two numbers is 6, and the sum of their squares is 28. Find these numbers exactly

Sigrid
4.5
$\left\{\begin{array} { l } x+y=6 \\ {x}^{2}+{y}^{2}=28\end{array} \right.$
$\left\{\begin{array} { l } x=6-y \\ {x}^{2}+{y}^{2}=28\end{array} \right.$
${\left$6-y \right$}^{2}+{y}^{2}=28$
$\begin{array} { l }y=3+\sqrt{ 5 },\\y=3-\sqrt{ 5 }\end{array}$
$\begin{array} { l }x=6-\left$3+\sqrt{ 5 } \right$,\\y=3-\sqrt{ 5 }\end{array}$
$\begin{array} { l }x=6-\left$3+\sqrt{ 5 } \right$,\\x=6-\left$3-\sqrt{ 5 } \right$\end{array}$
$\begin{array} { l }x=3-\sqrt{ 5 },\\x=6-\left$3-\sqrt{ 5 } \right$\end{array}$
$\begin{array} { l }x=3-\sqrt{ 5 },\\x=3+\sqrt{ 5 }\end{array}$
$\begin{array} { l }\left$x_1, y_1\right$=\left$3-\sqrt{ 5 }, 3+\sqrt{ 5 }\right$,\\\left$x_2, y_2\right$=\left$3+\sqrt{ 5 }, 3-\sqrt{ 5 }\right$\end{array}$
$\begin{array} { l }\left\{\begin{array} { l } 3-\sqrt{ 5 }+3+\sqrt{ 5 }=6 \\ {\left$3-\sqrt{ 5 } \right$}^{2}+{\left$3+\sqrt{ 5 } \right$}^{2}=28\end{array} \right.,\\\left\{\begin{array} { l } 3+\sqrt{ 5 }+3-\sqrt{ 5 }=6 \\ {\left$3+\sqrt{ 5 } \right$}^{2}+{\left$3-\sqrt{ 5 } \right$}^{2}=28\end{array} \right.\end{array}$
$\begin{array} { l }\left\{\begin{array} { l } 6=6 \\ 28=28\end{array} \right.,\\\left\{\begin{array} { l } 3+\sqrt{ 5 }+3-\sqrt{ 5 }=6 \\ {\left$3+\sqrt{ 5 } \right$}^{2}+{\left$3-\sqrt{ 5 } \right$}^{2}=28\end{array} \right.\end{array}$
$\begin{array} { l }\left\{\begin{array} { l } 6=6 \\ 28=28\end{array} \right.,\\\left\{\begin{array} { l } 6=6 \\ 28=28\end{array} \right.\end{array}$
$\begin{array} { l }\left$x_1, y_1\right$=\left$3-\sqrt{ 5 }, 3+\sqrt{ 5 }\right$,\\\left$x_2, y_2\right$=\left$3+\sqrt{ 5 }, 3-\sqrt{ 5 }\right$\end{array}$

Frequently asked questions $FAQs$
What fraction of the students in a class scored less than 70% on a test?
+
What is the domain of the square root function f$x$ = √$x+5$?
+
What is 3/4 of 72?
+