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Trava [24]
4 years ago
15

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

Mathematics
1 answer:
Musya8 [376]4 years ago
3 0

Answer:

16

Step-by-step explanation:

<u>Given:</u>

<u></u>x+y=6<u></u>

<u></u>xy =10<u></u>

<u>To find:</u>

<u></u>x^{2}+ y^{2} = ?<u></u>

<u></u>

<u>Formula:</u>

<u></u>(a+b)^2 =a^{2} +b^{2} +2ab<u></u>

<u></u>

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

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