Question

X + y is equals to 4 x y is equals to 2 x square + y square

Answer 1

Correct Question:

If (x+y) = 4 and (xy) = 2, then find the value of x² + y²

Answer:

Value of $\sf{x^2\:+\:y^2}$ is 12.

Explanation:

Given:

• (x+y) = 4
• (xy) = 2

To find :

• Value of (x²+y²)

Solution:

We know that,

$\large{\boxed{\sf{\red{(x+y)^2\:=\:x^2\:+\:y^2\:+2xy}}}}$

Putting the values,

: $\implies$ $\sf{(4)^2\:=\:x^2\:+\:y^2\:+2(2)}$

: $\implies$ 16 = $\sf{x^2\:+\:y^2\:+4}$

: $\implies$ 16 - 4 = $\sf{x^2\:+\:y^2}$

: $\implies$ $\large{\boxed{\blue{\sf{x^2\:+\:y^2\:=12}}}}$

$\therefore$ Value of $\sf{x^2\:+\:y^2}$ is 12.

Answer 2

Given:

• x + y = 4
• xy = 2

To find: The value of x² + y².

Answer:

Let's connect the data we have with an identity:

(x + y)² = x² + 2xy + y²

We know the value of x + y and xy [given]. Substituting them in the formula,

(4)² = x² + 2(2) + y²

16 = x² + 4 + y²

16 - 4 = x² + y²

12 = x² + y²

Other related identities:

(x - y)² = x² - 2xy + y²

(x - y)(x + y) = x² + y²

(x + y)³ = x³ + 3x²y + 3xy² + y³

x³ + y³ = (x + y)(x² - xy + y²)