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

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

Frequently asked questions (FAQs)
Math Question: "Simplify the expression 3x(4x + 7) - 2(6x - 5) using the distributive property."
+
What is the result of (2 + 3i) * (4 - i)?
+
What is the volume of a right circular cylinder with height 10 units and radius 5 units?
+
New questions in Mathematics
A=m/2-t isolate t
-442/c+5=26 what is c?
If L (-2, -5) reflected across y = -4. What are the coordinates of L?
132133333-33
The data set (75, 85, 58, 72, 70, 75) is a random sample from the normal distribution No(µ, σ). Determine a 95% two-sided confidence interval for the mean µ .
Director of reservations believes that 9% of the ticketed passengers are no-shows. If the directors right what is the probability that the proportion of no-shows in a sample of 789 ticketed passengers with differ from the population proportion buy more than 3% round your answer to four decimal places.
Suppose a large shipment of cell phones contain 21% defective. If the sample of size 204 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 4% round your answer to four decimal places
2x-4y=-6; -4y+4y=-8
Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows: (Raúl wins) = 20% (Gilberto wins) = 0.05% (Arturo wins) = ¾%. Perform operations and order events from least to most probable.
7=-4/3y -1
Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4336 patients treated with the​ drug, 194 developed the adverse reaction of nausea. Construct a ​99% confidence interval for the proportion of adverse reactions.
TEST 123123+1236ttttt
4+168×10³×d1+36×10³×d2=-12 -10+36×10³×d1+72×10³×d2=0
Determine the increase of the function y=4x−5 when the argument changes from x1=2 to x2=3
Solve equations by equalization method X-8=-2y 2x+y=7
Determine a general formula​ (or formulas) for the solution to the following equation.​ Then, determine the specific solutions​ (if any) on the interval [0,2π). cos30=0
A hardware bill totals $857.63 with discounts of 5% and 3%. What is the net cost of the Material ?
Two particles of electrical charges Q1=3.8×10-⁶C and q,=4.4×10-⁶C are separated in vacuum by a distance of 4.0.10-⁸ m. Since K=9.0.10⁹ N.m²/C², the intensity of the interaction force between them, in newtons, is?
What is the total amount due and the amount of interest on a 3-year loan of $1,000 at a simple interest rate of 12% per year?
Solve the following 9x - 9 - 6x = 5 + 8x - 9