SOLUTION: The product of two numbers is 8. The difference of their squares is 12. Find the two numbers.
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Question 675349: The product of two numbers is 8. The difference of their squares is 12. Find the two numbers.
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!
let one no is x
so the other no is 8/x
The difference of their squares is 12
so x^2-(8/x)^2=12
or x^2-64/x^2=12
or x^4-64=12x^2
or x^4-12x^2-64=0
or (x^4-12x^2+36)-36-64=0
or (x^2-6)^2=100
or x^2-6=+/-10
now two cases arise
1st x^2-6=-10
or x^2=-10+6=-4 (rejected for -ve value)
2nd x^2-6=+10
or x^2=10+6=16
or x=+/-2
so the other no is -/+4
ans
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