Quality Learning Support For Better Outcomes
First time here? Checkout the FAQs!
x
MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
7 views
Find 2 numbers that sum to 21 and the sum of the squares is 261.
in Mathematics by Diamond (80,748 points) | 7 views

1 Answer

0 like 0 dislike
There are two statements made, which can be written as two equations:
The sum of two numbers are $21: x+y=21$ The sum of the squares is $261: x^{2}+y^{2}=261$
We are asked to find $x$ and $y$.
Since we have the sums of the numbers and the sums of their squares; we can use the square formula of $x+y$, that
is:
$(x+y)^{2}=x^{2}+2 x y+y^{2} \ldots$ Here, we can insert the known values $x+y$ and $x^{2}+y^{2}$
$(21) 2=261+2 x y \ldots$ Arranging to find $x y:$ $441=261+2 x y$
$441-261=2 x y$
$180=2 x y$
$x y=180 / 2$
$x y=90$
We need to find two numbers which multiply to 90 . Checking the answer choices, we see that in (b), 15 and 6 are given, which sum to $90(15 * 6=90)$ and their squares sum to $261(152+62=225+36=261)$.
by Diamond (80,748 points)

Related questions

0 like 0 dislike
1 answer
1 like 0 dislike
2 answers
0 like 0 dislike
1 answer
0 like 0 dislike
2 answers

Join the MathsGee Answer Hub community and get study support for success - MathsGee Answer Hub provides answers to subject-specific educational questions for improved outcomes.



On MathsGee Answers, you can:


  1. Ask questions
  2. Answer questions
  3. Comment on Answers
  4. Vote on Questions and Answers
  5. Donate to your favourite users
  6. Create/Take Live Video Lessons

Posting on MathsGee


  1. Remember the human
  2. Behave like you would in real life
  3. Look for the original source of content
  4. Search for duplicates before posting
  5. Read the community's rules
MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

MathsGee ZOOM | eBook