Question

if x + y = 3, x^2 + y^2 = 5 then xy is​

Answer 1

Step-by-step explanation:

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Answer 2

ANSWER:

Given:

• x + y = 3
• x² + y² = 5

To Find:

• xy

Solution:

We know that,

⇒ (a + b)² = a² + b² + 2ab

We need to find the value of:

⇒ xy

So, substituting a for x and b for y,

⇒ (x + y)² = x² + y² + 2xy

⇒ (x + y)² = (x² + y²) + 2(xy)

We are given that,

⇒ x² + y² = 5

And,

⇒ x + y = 3

Now, substituting values of (x² + y²) and (x + y),

⇒ (x + y)² = (x² + y²) + 2(xy)

⇒ (3)² = (5) + 2(xy)

⇒ 9 = 5 + 2(xy)

⇒ 2xy = 9 - 5

⇒ 2xy = 4

⇒ xy = 2

Therefore, value of xy is 2.

Formula used:

• (a + b)² = a² + b² + 2ab