Question

10a2+ab/3ab-b2=10/1 what is a:b
​

Answer 1

SOLUTION

GIVEN

$\displaystyle\sf{ \frac{10 {a}^{2} + ab}{3ab - {b}^{2} } = \frac{10}{1} }$

TO DETERMINE

The value of a : b

EVALUATION

Here it is given that

$\displaystyle\sf{ \frac{10 {a}^{2} + ab}{3ab - {b}^{2} } = \frac{10}{1} }$

We simplify it as below :

$\displaystyle\sf{ \frac{10 {a}^{2} + ab}{3ab - {b}^{2} } = \frac{10}{1} }$

$\displaystyle\sf{ \implies \: 10 {a}^{2} + ab = 10(3ab - {b}^{2}) }$

$\displaystyle\sf{ \implies \: 10 {a}^{2} + ab = 30ab - 10{b}^{2} }$

$\displaystyle\sf{ \implies \: 10 {a}^{2} - 29 ab + 10{b}^{2} = 0}$

$\displaystyle\sf{ \implies \: 10 {a}^{2} - 25 ab - 4ab+ 10{b}^{2} = 0}$

$\displaystyle\sf{ \implies \: 5a(2a - 5b) - 2b(2a - 5b)= 0}$

$\displaystyle\sf{ \implies \:(2a - 5b) (5a - 2b)= 0}$

Now 2a - 5b = 0 gives 2a = 5b

Consequently a : b = 5 : 2

Again 5a - 2b = 0 gives 5a = 2b

Consequently a : b = 2 : 5

FINAL ANSWER

a : b = 5 : 2 or a : b = 2 : 5

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. 3a=5b and 6b=7c what is the value of a:b:c

https://brainly.in/question/31811491

2. Ifa : b=c:d=e: f= 2:1, then (a + 2c + 3e) : (5b + 10d + 15f) is equal to:

https://brainly.in/question/23293448

3. If p/2q = 11/5 then p-2q/p+2q = ?

https://brainly.in/question/34239839