Question

Seja x + y = 6. Qual é o valor positivo de x² + y², sabendo que xy = 10? * 14 15 16 17 18

Answer 1

Answer:

16

Step-by-step explanation:

Given:

$x+y=6$

$xy =10$

To find:

$x^{2}+ y^{2} = ?$

Formula:

$(a+b)^2 =a^{2} +b^{2} +2ab$

Here,

$a=x\\b=y$

Squaring both sides of: $x+y=6$

$\Rightarrow (x+y)^2 = 6^2$

Using formula written above on LHS:

$x^{2} +y^{2} +2xy = 36$

Given $xy=10$

$\Rightarrow x^{2} +y^{2} + 2 \times 10 = 36\\\Rightarrow x^{2} +y^{2} + 20= 36\\\Rightarrow x^{2} +y^{2}= 36-20\\\Rightarrow x^{2} +y^{2}= 16$

So, correct answer is:

$x^{2} +y^{2} = 16$