Question

If x2 + y2 =9 and xy = 8, find x+y

Answer 1

Answer:

5

Step-by-step explanation:

$(x+y)^2 = x^2 + y^2 + 2xy\\\\(x+y)^2 = 9 + (2*8)\\\\(x+y)^2 = 9 + 16\\\\(x+y)^2 = 25\\\\x+y = \sqrt{25}\\\\x+y = 5$

Hope it helps you mate :)

Answer 2

Answer :

x + y = 5

Note :

★ (a + b)² = a² + 2ab + b²

★ (a - b)² = a² - 2ab + b²

★ (a + b)(a - b) = a² - b²

★ (a + b)² = (a - b)² + 4ab

Solution :

• Given : x² + y² = 9 , xy = 8
• To find : x + y = ?

We know that ;

=> (x + y)² = x² + 2xy + y²

=> (x + y)² = x² + y² + 2xy

=> (x + y)² = 9 + 2•8

=> (x + y)² = 9 + 16

=> (x + y)² = 25

=> (x + y)² = 25

=> x + y = √25

=> x + y = 5

Hence , x + y = 5 .