ABC26GN1208 · Simplification

Subject: General Aptitude · Chapter: Simplification · Exam: · Marks: · Difficulty:

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

Answer (as printed): C

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.

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