Question

solve if 5x^2-13xy+6y^2=0 then x:y is

Answer 1

Answer:

x : y is 3 : 5 or 2 : 1 .

Step-by-step explanation:

Given equation : 5x^2 - 13xy + 6y^2 = 0

= >  5x^2 -13xy + 6y^2 = 0

= >  5x^2 + 6y^2 = 13xy

= >  { 5x^2 / xy } + { 6y^2 / xy } = 13

= > ( 5x / y ) + ( 6y / x ) = 13

Let. x / y = a and y / x = 1 / a ( as it is the reciprocal of x / y ).

= > 5a + 6 / a = 13

= >  ( 5a^2 + 6 ) = 13a

= >  5a^2 - 13a + 6 = 0

= >  5a^2 - ( 10 + 3 )a + 6 = 0

= >  5a^2 - 10a - 3a + 6 = 0

= >  5a( a - 2 ) - 3( a - 2 ) = 0

= >  ( a - 2 )( 5a - 3 ) = 0

= >  a - 2 = 0 ...or... 5a - 3 = 0

= > a = 2  ...or... a = 3 / 5

Thus,

→ a = 2 ⇒ x / y = 2 / 1

→ x / y = 3 / 5

Hence,

x : y is 3 : 5 or 2 : 1 .

Answer 2

Answer: 3 : 5 or 2 : 1. the factors are 10 and 3