Question

if 5x-7y=19 and xy=-2,then the value of 25x²+49y² is equal to
A:210
B:215
C:218
D:221​

Answer 1

Answer:

first square 5x-7y = square of 19 , now 25x square +49y square - 70xy = 361 , now put the value of xy=-2 in the equation , so 25x squre + 49y square - 70*-2 =361 , now transport the values , so = 25 x2 + 49 y2=361-140 = 221 , if ans is correct brainlist my ans and connect to me and give me 5 stars pls

Answer 2

The value of 25x² + 49y² is equal to 221.

Given,

the following two equations:

5x - 7y = 19

xy = -2

To Find,

25x² + 49y² = ?

Solution,

The solution for this problem are as follows:

We have been given the following two equations:

5x - 7y = 19 → Let this be equation (1).

xy = -2 → Let this be equation (2).

These are equations in two variables x and y.

Multiply equation 1 throughout by y:

⇒ 5xy - 7y² = 19y → Let this be equation (3).

Now substitute equation (1) in equation (3):

⇒ 5(-2) - 7y² = 19y

⇒ -10 - 7y² = 19y

⇒ 7y² + 19y + 10 = 0

The above equation is a quadratic equation in two variables.

Its solution is given by y = (-b ± √(b² - 4ac))/2a

Here, a = 7, b = 19, c = 10.

⇒ y = (-19 ± √(19² - 4×7×10))/(2×7)

⇒ y = (-19 ± √(361 - 280))/14

⇒ y = (-19 ± √81)/14

⇒ y = (-19 ± 9)/14

⇒ y = (-19 + 9)/14 and y = (-19 - 9)/14

⇒ y = -10/14 and y = -28/14

⇒ y = -0.714 and y = -2

Hence, the integral value of y = -2.

Substituting the value of y in equation (1), we get:

⇒ 5x - 7(-2) = 19

⇒ 5x + 14 = 19

⇒ 5x = 19 - 14

⇒ 5x = 5

⇒ x = 1

The value of 25x² + 49y² becomes

⇒ 25(1)² + 49(-2)²

⇒ 25(1) + 49(4)

⇒ 25 + 196

⇒ 221

Therefore, 25x² + 49y² = 221.

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