1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
miss Akunina [59]
3 years ago
13

Use the identity (x^2+y^2)^2=(x^2−y^2)^2+(2xy)^2 to determine the sum of the squares of two numbers if the difference of the squ

ares of the numbers is 5 and the product of the numbers is 6.
Mathematics
1 answer:
marissa [1.9K]3 years ago
5 0

Answer:

Step-by-step explanation:

(x^2+y^2)^2=(x^2)^2+2x^2y^2+(y^2)^2

Adding and substracting 2x^2y^2

We get

(x^2+y^2)^2=(x^2)^2+2x^2y^2+(y^2)^2 +2x^2y^2-2x^2y^2

And we know a^2-2ab+b^2=(a-b)^2

So we identify (x^2)^2 as a^2 ,(y^2)^2 as b^2 and -2x^2y^2 as - 2ab. So we can rewrite (x^2+y^2)^2=(x^2 - y^2)^2 + 2x^2y^2 + 2x^2y^2= (x^2 - y^2)^2+4x^2y^2= (x^2 - y^2)^2+2^2x^2y^2

Moreever we know (a·b·c)^2=a^2·b^2·c^2 than means 2^2x^2y^2=(2x·y)^2

And (x^2+y^2)^2=(x^2 - y^2)^2 + (2x·y)^2

You might be interested in
Whats 95 closer to 64 or 125
Basile [38]
125-95=30
95-64=31
so it would be 125
6 0
3 years ago
Please help me babes!!
abruzzese [7]
The correct answer would be C) CBA-EFD 
6 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=12%20%5Cfrac%7B3%7D%7B6%7D%20%2B%2014%5Cfrac%7B4%7D%7B6%7D%20" id="TexFormula1" title="12 \fra
Vikki [24]
27 1/6 or 163/6 or 27.16
6 0
3 years ago
Read 2 more answers
Solve the system of equations 4x+5y=-1 and -5x-8y=10 by combining the equations.
Flura [38]

The solutions to the given system of equations are x = 6 and y = -5

<h3>Simultaneous linear equations</h3>

From the question, we are to solve the given system of equations

The given system of equation is

4x+5y=-1

-5x-8y=10

Multiply the <u>first equation</u> by 5 and the <u>second equation</u> by 4

5× (4x+5y=-1)

4× (-5x-8y=10)

20x + 25y = -5

-20x - 32y = 40

------------------------

0x + (-7y) = 35

-7y = 35

y = 35/-7

y = -5

Substitute the value of y into the first equation to find x

4x + 5y = -1

4x + 5(-5) = -1

4x -25 = -1

4x = -1 +25

4x = 24

x = 24/4

x = 6

Hence, the solutions to the given system of equations are x = 6 and y = -5

Learn more on Simultaneous linear equation here: brainly.com/question/12647791

#SPJ1

3 0
2 years ago
Which congruence theorems can be used to prove EFG congruent to JHG
MatroZZZ [7]

SAS you have two pairs of parallel sides

you have another pair of side congruent to one another

and angle G is the same to itself.

3 0
3 years ago
Other questions:
  • Pls help with this question. I will give brainliest answer :)
    7·2 answers
  • Find the circumference of C in terms of π<br>radius of c Is 5​
    14·2 answers
  • Find the distance represented by a 3-inch line on a blueprint with a scale of 3/8 inch = 1 foot
    10·1 answer
  • 1. If a - b = 4 and a + b = 12, what is the<br> value of a?
    15·1 answer
  • The sum of -2 and three times a number
    15·1 answer
  • Solve -5(x-7)^2+30=-20
    12·1 answer
  • Given an equation y= -8x -4. Identify the slope and y-intercept
    10·1 answer
  • Pleaseeee answer asappppp
    15·1 answer
  • Farmers have learned how to grow watermelons
    15·1 answer
  • Which of the following represents discrete data? Question 7 options: The number of beads in a jar The volume of water in a glass
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!