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kifflom [539]
3 years ago
10

If x and y are two positive real numbers such that x 2 +4y 2 =17 and xy =2, then find the value of x- 2y. a. 3 b. 4 c. 8 d. 9

Mathematics
1 answer:
Dafna11 [192]3 years ago
7 0

Answer: The value of x- 2y is a. \pm 3.

Step-by-step explanation:

Given:  x and y are two positive real numbers such that x^2+4y^2=17   and xy= 2 .

Consider (x-2y)^2=x^2-2(x)(2y)+(2y)^2\ \ \ [(a+b)^2=(a^2-2ab+b^2)]

=x^2-4xy+4y^2

=x^2+4y^2-4(xy)

Put  x^2+4y^2=17   and xy= 2 , we get

(x-2y)^2=17-4(2)=17-8=9

\Rightarrow\ (x-2y)^2=9

Taking square root on both sides , we get'

x-2y= \pm3

Hence, the value of x- 2y is a. \pm 3.

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MrRa [10]

8 and 9

8^3 = 512

9^3 = 729

512 + 729 = 1241

3 0
2 years ago
Can someone please help me?
Vladimir79 [104]

Answer:

<h3> ( - 1 , - 1 )</h3>

Option D is the correct option.

Step-by-step explanation:

y = - 2x - 3 → Equation ( i )

y = 3x + 2 → Equation ( ii )

Using elimination method

y + 2x = - 3

y - 3x = 2

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

5x = - 5

Divide both sides of the equation by 5

\frac{5x}{5}  =  \frac{ - 5}{5}

Calculate

x =  - 1

Again, Putting the value of x in equation ( ii ) in order t get the value of y

y = 3x + 2

plug the value of x

= 3  \times ( - 1) + 2

Any expression multiplied by ( - 1 ) equals it's opposite

=  - 3 + 2

Calculate

=  - 1

Therefore, The possible solution of the system is the ordered pair ( x , y )

(x \:, y \: ) =  ( - 1 \:, - 1)

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

Check if the given ordered pair is the solution of the system of equation

- 1 =  - 2 \times ( - 1)  - 3

- 1 = 3 \times ( - 1) + 2

Simplify the equation

- 1 =  - 1

- 1 =  - 1

Since all the equalities are true, the ordered pair is the solution of the system.

<h3>( x , y ) = ( - 1 , - 1 )</h3>

Hope this helps..

Best regards!!

7 0
3 years ago
The sum of a number and 3 is 8
Doss [256]

Answer:

5

Step-by-step explanation:

5 0
2 years ago
a regular polygon has a perimeter of 36 inches. each side is exactly 6 inches long. which figure does this discribe?
fgiga [73]
Since a side is only 6 inches long and the total perimeter is 36; take 36/6 and you get 6. The only figure with six sides is a hexagon, thus your answer is hexagon.
3 0
3 years ago
What is the partial product for 1,600 and 280
Likurg_2 [28]

Answer:

Hope this helps!

Step-by-step explanation:

4 0
2 years ago
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