If15(2x*x-y*y)=7xy,find x:y; if x and y both are positive.
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15(2x*x-y*y)=7xy
dividing both side by y∧2 we get
15(2x∧2/y∧2-1)=7x/y
Let x/y=a
15(2a∧2-1)=7a
30a∧2-7a-15=0
30a∧2-25a+18a-15=0
5a(6a-5)+3(6a-5)=0
(5a+3)(6a-5)=0
a=-3/5 or 5/6
or
x/y=-3/5 or 5/6 but x and y are both positive so x/y can never be negative
so we get
x:y=5:6
dividing both side by y∧2 we get
15(2x∧2/y∧2-1)=7x/y
Let x/y=a
15(2a∧2-1)=7a
30a∧2-7a-15=0
30a∧2-25a+18a-15=0
5a(6a-5)+3(6a-5)=0
(5a+3)(6a-5)=0
a=-3/5 or 5/6
or
x/y=-3/5 or 5/6 but x and y are both positive so x/y can never be negative
so we get
x:y=5:6
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