a2+b2=45,b2+c2=40 then a,b,c=?

Question

a2+b2=45,b2+c2=40 then identify a,b,c=?

Answer 1

1.) a^2+b^2=45 2.) b^2+c^2=40 then a,b,c=? in equation 1 solve for b^2 1.) b^2 = 45 - a^2 in equation 2.) solve for b^2 2.) b^2 = 40 - c^2 sert equal to each others 45 - a^2 = 40 - c^2 5 = a^2 - c^2 a^2 = 5 + c^2 or c^2= a^2 - 5 2a^2 = 5; a^2 = 5/2; a = sqrt(5/2) = c use the orginal equations: 1.) a^ + b^2=45; c^2 + b^2 + 5 = 45; c^2 + b^2 = 40 2.) b^2+c^2=40; a^2 + b^2 - 5 = 40; a^2 + b^2 = 40; therefore; c^2 = a^2 a = c = sqrt(5/2) using equation 1.) 5/2 + b^2 = 45 5 + 2b^2 = 90 2 b^2 = 85 b^2 = 85/2 b = sqrt(85/2) a = c = sqrt(5/2)