Question

Find the value of
x^2 - 4x+y^2-9y+13=0

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Question:

If x² - 4x + y² - 9y + 13 = 0, find the value of ( x + y ).

Answer:

The value of ( x + y ) is 11.19 or 1.09.

Step-by-step-explanation:

The given equation is

x² - 4x + y² - 9y + 13 = 0

We have to find the value of ( x + y ).

Now,

x² - 4x + y² - 9y + 13 = 0

⇒ x² - 4x = - y² + 9y - 13

⇒ x² - 4x = - ( y² - 9y + 13 )

⇒ y² - 9y + 13 = - ( x² - 4x )

⇒ y² - 9y + 13 = - x² + 4x

Comparing with ay² + by + c = 0,

- x² + 4x = 0

⇒ 4x = x²

⇒ 4 = x² / x

⇒ x = 4

Now, by substituting x = 4 in the equation

y² - 9y + 13 = - x² + 4x

⇒ y² - 9y + 13 = - ( 4 )² + 4 * 4

⇒ y² - 9y + 13 = - 16 + 16

⇒ y² - 9y + 13 = 0

Comparing with ay² + by + c = 0, we get,

• a = 1
• b = - 9
• c = 13

Now,

b² - 4ac = ( - 9 )² - 4 * 1 * 13

⇒ b² - 4ac = 81 - 52

⇒ b² - 4ac = 29

Now, by quadratic formula,

y = [ - b ± √( b² - 4ac ) ] / 2a

⇒ y = [ - ( - 9 ) ± √29 ] / ( 2 * 1 )

⇒ y = ( 9 ± √29 ) / 2

⇒ y = ( 9 + √29 ) / 2 OR y = ( 9 - √29 ) / 2

• √29 = 5.385

⇒ y = ( 9 + 5.385 ) / 2 OR y = ( 9 - 5.385 ) / 2

⇒ y = 14.385 / 2 OR y = 3.615 / 2

⇒ y = 7.1925 OR y = 1.0875

If y = 7.1925, then

x + y = 4 + 7.1925

⇒ x + y = 11.1925

⇒ x + y = 11.193

⇒ x + y ≈ 11.19

If y = 1.0875, then

x + y = 4 + 1.0875

⇒ x + y = 1.088

⇒ x + y = 1.09

⇒ x + y ≈ 1.09

∴ The value of ( x + y ) is 11.19 or 1.09.