If \( \Large x-y=1\ and\ x^{2}+y^{2}=41, \), then value of x+y will be
Correct Answer: Description for Correct answer:
Given \( \Large x-y = 1\ or\ x = 1 + y \)
and \( \Large x^{2}+y^{2} = 41 \)
Substituting value of x from equation (i) in equation (ii), we get
\( \Large \left(1+y\right)^{2}+y^{2}=41 \)
=> \( \Large 2y^{2}+2y +1 = 41\)
=> \( \Large 2y^{2}+2y-40 = 0 \)
=> \( \Large \left(y+5\right) \left(y-4\right) = 0 \)
Therefore, y = -5 or 4
From equation (i)
x = -4 or 5
Therefore, x+y = -9 or 9
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