Question 213913
4(X+100)^2+4X^2=3080^2
4(X^2+200X+10,000)+4X^2=9,486,400
4X^2+800X+40,000+4X^2=9,486,400
8X^2+800X+40,000-9,486,400=0
8X^2+800X-9,446,400=0
8(X^2+100X-1,180,800)=0
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
X=(-100+-SQRT[100^2-4*1*-1,180,800])/281
X=(-100+-SQRT[10,000+4,723,200])/2
X=(-100+-SQRT4,733,200)/2
X=(-100+-2,175.5918)/2
X=(-100+2,175.5918)/2
X=2,075.5918/2
X=1,037.8 ANS. FOR THE SLOWER PLANE.
1,037.8+100=1,137.8 ANS. FOR THE FASTER PLANE.
PROOF:
4(1,137.8)^2+4*1,037.8^2=3080^2
4*1,294,588.8+4*1,077,028.8=9,486,400
5,178,355.2+4,308,115.2=9,486,400
9,486,400~9,486,400