Question

If
$x - y = 7$
and
$xy = 9$
,find the value of
${x }^{2} + {y}^{2}$
.
First answer will get 50 points and will be marked as brainliest......answer fast......
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Answer 1

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

$\sf{x - y = 7 \qquad (Given)}$

$\sf{xy = 9 \qquad (Given)}$

$\sf{Putting \ values, \ we \ get}$

$\sf{(7)^2 = x^2 + y^2 - 2(9)}$

$\sf{49 = x^2 + y^2 - 18}$

$\sf{x^2 + y^2 = 49 + 18 = 67}$

$\sf\red{The \ value \ of \ x^2 + y^2 \ is \ 67.}$

Answer 2

Given

x-y=7

xy=9

Using Identity=(a-b)²=a²+b²-2ab

Just Like

(x-y)²=x²+y²-2xy

7²=x²+y²+2×9. [ (x-y=7)(xy=9)]

49=x²+y²-18

x²+y²=49+18

x²+y²=67

$\boxed{\mathtt{\huge{{x}^{2}+{y}^{2}=67}}}$