Question

if (a,0),(0,b)and(1,1)are three points,show that 1/a+1/b=1​

Answer 1

$\frac{1}{a}$ + $\frac{1}{b}$ = 1, it is proved.

Step-by-step explanation:

Given, (x_1 = a, y_1 = 0), (x_2 = 0, y_2 = b) and (x_3 = 1, y_3 = 1)

∴ Area of triangle

= $\frac{1}{2}$ × {x_1(y_2 - y_3 ) + x_2(y_3 - y_1) +x_3(y_1 - y_2 )} = 0

⇒ x_1(y_2 - y_3 ) + x_2(y_3 - y_1) +x_3(y_1 - y_2 ) = 0

⇒ a(b - 1) + 0(1 - 0) + 1(0 - b) = 0

⇒ ab -a  - b = 0

⇒ a  + b = ab     ..... (1)

Dividing both sides "ab" equation (1), we get

$\frac{a + b}{ab}$ = $\frac{ab}{ab}$

∴ $\frac{1}{a}$ + $\frac{1}{b}$ = 1, it is proved.