Question

14. If x - y = 8, xy = 2, find x² + y2.​

Answer 1

Answer:

68

Step-by-step explanation:

(x-y)^2= (x^2+y^2) -2xy

8^2=(x^2+y^2)-4

64=(x^2+y^2 )-4

68=x^2+y^2

Answer 2

QUESTION :

If x - y = 8, xy = 2, find x² + y².

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Given :

• x - y = 8

• xy = 2

To find :

• x² + y²

Formula used :

${(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy$

Solution :

We know that :-

${(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy$

Now put :-

• x - y = 8
• xy = 2

$\implies {(8)}^{2} = {x}^{2} + {y}^{2} - 2(2)$

$\implies 64 = {x}^{2} + {y}^{2} - (2 \times 2)$

$\implies 64 = {x}^{2} + {y}^{2} - 4$

$\implies 64 + 4= {x}^{2} + {y}^{2}$

$\implies 68= {x}^{2} + {y}^{2}$

Answer : 68

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$\large\bf\blue{Additional-Information}$

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

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

$\implies{(a+b)^3 = a^3 + b^3 + 3ab(a + b)}$

$\implies{(a-b)^3 = a^3 - b^3 - 3ab(a-b)}$

$\implies{(a^3+b^3)= (a+b)(a^2 - ab + b^2)}$

$\implies{(a^3-b^3)= (a-b)(a^2 + ab + b^2)}$

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