Question

If $x+y=2$ and $\frac{1}{x}+\frac{1}{y}=2\frac{1}{4}$ then $x$ is

• A. $\frac{4}{3}$
• B. $2\frac{1}{4}$
• C. $\frac{2}{3}$
• D. either (1) or (3)

Answer 1

Answer: (D)

either (1) or (3)

$\frac{1}{x}+\frac{1}{y}=2\frac{1}{4}$
$y+x=\frac{9}{4}xy$
Given $x+y=2$, $x=2-y$
Then $2-y+x=\frac{9}{4}x(2-x)$
$8=9(2x-x^2)$
$9x^2-18x+8=0$
$9x^2-12x-6x+8=0$
$3x(3x-4)-2(3x-4)=0$
$(3x-2)(3x-4)=0$
$x=\frac{2}{3}$ and $x=\frac{4}{3}$