Question

If x square + y square is equal to 9 and x*y = 8 find the value of x+y

Answer 1

Answer:

±5

Step-by-step explanation:

x² + y² = 9

xy = 8

now, (x + y)² = (x² + y²) + 2(xy)

⇒ (x + y)² = 9 + 2(8) = 9 + 16 = 25

=> x + y = ±5 (answer)

Answer 2

Given :

• x² + y² = 9
• x y = 8

To find :

• ( x + y ) = ?

Solution :

Using algebraic identity

→ ( x + y )² = x² + y² + 2 x y

→ ( x + y )² = ( x² + y )² + 2 ( x y )

substituting given values

→ ( x + y )² = ( 9 ) + 2 ( 8 )

→ ( x + y )² = 9 + 16

→ ( x + y )² = 25

→ ( x + y ) = √25

→ ( x + y ) = ± 5

Therefore,

• Value of x + y would be ±5 .

Know more algebraic identities:

• (a - b)² = a² + b² - 2 a b
• a² - b² = ( a + b ) ( a - b )
• ( x + a ) ( x + b ) = a² + x ( a + b ) + ab
• ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca
• (a + b)³ = a³ + b³ + 3ab (a + b)
• (a - b)³ = a³ - b³ - 3ab (a - b)
• a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)