SOLUTION: {{{ for which value satisfies the equation 10*a^2-b^2=1 when a is greater 40 and b is greater than 100}}}

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Question 750058:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
For which value satisfies the equation 10a%5E2-b%5E2=1 when a is greater 40 and b is greater than 100?
:
Rearrange to
10a^2 = b^2 + 1
a^2 = %28b%5E2%2B1%29%2F10
:
a = sqrt%28%28b%5E2%2B1%29%2F10%29
let a > 40
sqrt%28%28b%5E2%2B1%29%2F10%29 > 40
Square both sides
%28b%5E2%2B1%29%2F10%29 > 1600
b^2 + 1 > 1600 * 10
b^2 > 16000-1
b > sqrt%2815999%29
b = 127
Find a
10a^2 = b^2 + 1
10a^2 = 127^2 + 1
10a^2 = 16129 + 1
a^2 = 16130/10
a^2 = 1613
a = sqrt%281613%29
a = 40.162