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Required value of x / y is 4 / 17 or 1 / 2.
Step-by-step explanation:
Given,
34x^2 - 25xy + 4y^2 = 0
On dividing both sides by y^2 :
= > ( 34x^2 - 25xy + 4y^2 ) / y^2 = 0 / y^2
= > 34( x^2 / y^2 ) - 25( xy / y^2 ) + 4( y^2 / y^2 ) = 0 { y ≠ 0 }
= > 34( x / y )^2 - 25( x / y ) + 4( 1 ) = 0
= > 34( x / y )^2 - 25( x / y ) + 4 = 0
Let x / y = a, so x^2 / y^2 = a^2
= > 34a^2 - 25a + 4 = 0
= > 34a^2 - ( 8 + 17 )a + 4 = 0
= > 34a^2 - 8a - 17a + 4 = 0
= > 2a( 17a - 4 ) - ( 17a - 4 ) = 0
= > ( 17a - 4 )( 2a - 1 ) = 0
Using zero product rule,
17a - 4 = 0 or 2a - 1 = 0
a = 4 / 17 or a = 1 / 2
x / y = 4 / 17 or x / y = 1 / 2
Hence the required value of x / y is 4 / 17 or 1 / 2.
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