Question : If $xy=48$ and $x^2+y^2=100$, then $(x+y)$ is:
Option 1: 12
Option 2: 16
Option 3: 18
Option 4: 14
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Correct Answer: 14
Solution :
Given: $xy = 48$ and $x^{2}+y^{2} = 100$
We know the algebraic identity, $(x+y)^{2} = x^{2}+y^{2}+2xy$
By substituting the values in the above equation, we get:
$⇒(x+y)^{2} = 100+2×48$
$⇒(x+y) = \sqrt{196}$
$\therefore (x+y) = 14$
Hence, the correct answer is 14.
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