Question

$x$ and $y$ are defined such that $x^2 + y^2 = 0.1$ and $|x-y| = 0.2$. Find $|x| + |y|$.

• A. 0.3
• B. 0.4
• C. 0.2
• D. 0.6

Hint:

Use $(x\pm y)^2$ expansions with given sums/products to find required expressions.

Answer 1

The Correct Option is B

From $(x-y)^2 = 0.04 \ \Rightarrow \ x^2 - 2xy + y^2 = 0.04$. Given $x^2 + y^2 = 0.1$, subtract: $0.1 - 2xy = 0.04 \ \Rightarrow \ 2xy = 0.06 \ \Rightarrow \ xy = 0.03$. $(x+y)^2 = x^2 + y^2 + 2xy = 0.1 + 0.06 = 0.16$. So $|x+y| = 0.4$. For $x,y$ both positive or both negative, $|x|+|y| = |x+y| = 0.4$. \[ \boxed{0.4} \]