If x-y=1 and x²+y²=41, then the value of x+ y will be · ABC26GN1208
Subject: General Aptitude · Chapter: Simplification
If $x-y=1$ and $x^{2}+y^{2}=41$, then the value of $x+$ $y$ will be
(a)5 or 4
(b)- 5 or - 4
(c)± 9
(d)± 1
Answer
Explanation
$$\begin{gathered} x-y=1 \Rightarrow(x-y)^{2}=1 \Rightarrow x^{2}+y^{2}-2 x y=1 \\ \Rightarrow 41-2 x y=1 \Rightarrow 2 x y=40 . \\ \therefore \quad(x+y)^{2}=x^{2}+y^{2}+2 x y=41+40=81 \\ \Rightarrow(x+y)= \pm 9 . \end{gathered}$$
Explanation as extracted from the printed page; notation may be imperfect.
Study loop for Simplification
· Browse this chapter in the app