Question

if a+b/a-b=19/13 then a/b=?​

Answer 1

Answer:

Given,

a + b = 6 …… (1)

a - b = 4 ……. (2)

Method 1: (easiest)

add equation (1) and (2), we get

2a = 6 + 4

=> 2a = 10

=> a = 5

substitute value of a in either of equation (1) or (2),

=> b = 1

Hence ab = 5.1 = 5

————-

Method 2:

we know

(a+b)ˆ2 = aˆ2 + bˆ2 + 2ab

(a-b)ˆ2 = aˆ2 + bˆ2 - 2ab

subtracting equation 2 from 1, we get

(a+b)ˆ2−(a−b)ˆ2=(aˆ2+bˆ2+2ab)−(aˆ2+bˆ2−2ab)

=>(a+b)ˆ2−(a−b)ˆ2=aˆ2+bˆ2+2ab−(aˆ2+bˆ2−2ab)

=>(a+b)ˆ2−(a−b)ˆ2=aˆ2+bˆ2+2ab−aˆ2−bˆ2+2ab