Question

if a:b=5:4 and a^2-b^2=36
what is the solution

Answer 1

Answer:

a , b = 10 , 8  

or  -10 , -8

Step-by-step explanation:

a:b = 5:4

a/b = 5/4

a = 5b/4

a^2 - b^2 = 36

(5b/4)^2 - b^2 = 36

25 b^2 / 16  - b^2 = 36

25b^2 - 16b^2 = 36*16

9 b^2 = 36 * 16

b^2 = 4 * 16

b^2 = 64

b = +/- 8

a = 5b/4

a = 5(+/- 8)/4 = +/-10

Answer 2

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  

=>(a+b)ˆ2−(a−b)ˆ2=4ab ………… (3)

substituting the values of a+b and a-b in the equation (3) above, we have

=>6ˆ2−4ˆ2=4ab  

=>36−16=4ab  

=>20=4ab  

=>4.5=4ab  

=>ab=5  

Hence ab = 5