SOLUTION: the product of two positive numbers is 1, and the sum of their squares is 82/9. Find these numbers. (My last post didn't supply enough info, sorry.)

Question 142126: the product of two positive numbers is 1, and the sum of their squares is 82/9. Find these numbers. (My last post didn't supply enough info, sorry.)
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let b be one and s be the other.
bs=1
b^2+s^2=82/9
.
b=1/s
(1/s)^2+s^2=82/9
1/s^2 + s^2=82/9
9+9s^4=82s^2
9s^4-82s^2+9=0
9s^4-81s^2-s^2+9=0 Factoring by grouping.
9s^2(s^2-9)-(s^2-9)=0
(9s^2-1)(s^2-9)=0
(3s+1)(3s-1)(s+3)(s-3)=0
3s=1 s=1/3
s=3
.
Check:
3* 1/3 = 1 true
3^2+(1/3)^2=9 1/9 =82/9 true
.
Ed

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