SOLUTION: which pair of numbers has a difference of 8 and the difference of their squares is 20 more than 13 times the larger number? => i had already tried to solve it seems i can't sati

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Question 401995: which pair of numbers has a difference of 8 and the difference of their squares is 20 more than 13 times the larger number?
=> i had already tried to solve it seems i can't satisfy the expression. here is what i derived at:
a=larger number
a-b=8
a^2-b^2=20+13a
a=8+b
then substitute
(8+b)^2-b^2=20+13(8+b)
(64+b^2)-b^2=20+104+13b
then i simplify canceled the b^2 and get the value of b by transposing
i get an answer b=4.615 but i cant balance the equation when i substitute the value

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There's one problem, %288%2Bb%29%5E2 does NOT equal 64%2Bb%5E2


It turns out that %288%2Bb%29%5E2=64%2B16b%2Bb%5E2 for all values of b