MathematicsThe equation of a line having intercepts a,b on the axes such that a+b=5,ab=6 is

The equation of a line having intercepts $a, b$ on the axes such that $a + b = 5, a b = 6$ is

A
$2 x + 3 y - 6 = 0$
B
$3 x + 2 y - 6 = 0$
C
$2 x + 10 y - 5 = 0$
D
$10 x + 2 y - 5 = 0$

Solution:

a + b = 5, a b = 6

${(a - b)}^{2} = {(a + b)}^{2} - 4 a b \Rightarrow {(a - b)}^{2} = {(5)}^{2} - 4 \times 6 \Rightarrow a - b = 1$

By simplifying $a + b = 5$ , $a - b = 1$ $a = 3, b = 2$

Equation of the line is $\frac{x}{3} + \frac{y}{2} = 1 \Rightarrow 2 x + 3 y - 6 = 0$ (when $a$ is x-intercept, $b$ is y-intercept)

$\frac{x}{2} + \frac{y}{3} = 1 \Rightarrow 3 x + 2 y - 6 = 0$ (when $a$ is y-intercept, $b$ is x-intercept)

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