Question

if (x+y) = 7 and xy = 5 find the value of (x² + y²) ​

Answer 1

Answer:

The answer is 39

Step-by-step explanation:

Given $x+y=7$ and $xy=5$

Using the algebraic identity

    $(x+y)^2=x^2+y^2+2xy$

$\Rightarrow 7^2=x^2+y^2+2(5)\\\Rightarrow x^2+y^2=7^2-10=49-10=39$

Answer 2

EXPLANATION.

⇒ x + y = 7. - - - - - (1).

⇒ xy = 5. - - - - - (2).

As we know that,

Formula of :

⇒ (a² + b²) = (a + b)² - 2ab.

Put the values in the equation, we get.

⇒ (x² + y²) = (x + y)² - 2xy.

⇒ (x² + y²) = (7)² - 2(5).

⇒ (x² + y²) = 49 - 10.

⇒ (x² + y²) = 39.

                                                                                                                     

MORE INFORMATION.

(1) (x + y)² = x² + y² + 2xy.

(2) (x - y)² = x² + y² - 2xy.

(3) (x² - y²) = (x + y)(x - y).

(4) (x² + y²) = (x + y)² - 2xy.

(5) (x³ - y³) = (x - y)(x² + xy + y²).

(6) (x³ + y³) = (x + y)(x² - xy + y²).

(7) (x + y)³ = x³ + 3x²y + 3xy² + y³.

(8) (x - y)³ = x³ - 3x²y + 3xy² - y³.