Question

If x + y = 6 and x - y = 4, find () x2 + y2 (ii) xy.
Hint (1) 4xy = (x + y)2 - (x - y)2​

Answer 1

Answer:

x² + y² = 26

xy = 5

Step-by-step explanation:

Given that:

x + y = 6

x - y = 4

(i) x² + y² = ?

(ii) xy = ?

Use the hint: 4xy = (x + y)² - (x - y)²

⇒ 4xy = (6)² - (4)²

⇒ 4xy = 36 - 16 = 20

⇒ xy = 20/4

⇒ xy = 5

x + y = 6

⇒ (x + y)² = (6)²

⇒ x² + y² + 2xy = 36

⇒ x² + y² + 2×5 = 36

⇒ x² + y² + 10 = 36

⇒ x² + y² = 36 - 10

⇒ x² + y² = 26

Answer 2

QUESTIONS:

If x + y = 6 & x - y = 4 , the find

• (i) x² + y²
• (ii) xy

GIVEN:

• x + y = 6
• x - y = 4
• Hint: 4xy = (x + y)² - (x - y)²

SOLUTION:

Using the given hint

4xy = (x + y)² - (x - y)²

Substituting the value of x + y & x - y

→ 4xy = 6² - 4²

→ 4xy = 36 - 16

→ 4xy = 20

→ xy = 20/4

→ xy = 5

xy = 5

Finding x² + y²

Using

a² + b² = (a + b)² - 2ab

Similarly

x² + y² = (x + y)² - 2xy

Substituting the values of x + y & xy

→ x² + y² = 6² - 2(5)

→ x² + y² = 36 - 10

→ x² + y² = 26

x² + y² = 26

Hence, xy = 5 & x² + y² = 26