Question

If (6a

2

– ab) : (2ab – b

2

) = 6 : 1, find a : b.​

Answer 1

Answer:

first we can convert this into..

(6a^2 - ab) / (2ab - b^2) = 6/1 since r.h.s and l.h.s are ratios

ni we can cros multiply the expression

6a^2 -ab = 12ab - 6b^2

then we can divide the both sides from b^2

6 (a^2/b^2) - (a/b) = 12(a/b) - 6

now lets subtitute

t = (a/b)

then we can get the equation

6t^2 - 13t + 6 =0

6t^2 -4t -9t + 6 =0

2t( 3t - 2) -3(3t -2) =0

(3t -2)(2t -3) =0

sooo

t = 2/3 or t= 3/2

which means

a/b = 2/3 or a/b = 3/2

a:b = 2:3 or a:b = 3:2

both answers satisfy the 1st expression

hope this will help you :)

Step-by-step explanation: