To solve the given system of equations simultaneously, we can set the two expressions for cos(145) and cos(225) equal to each other and then solve for the variables:
(10000 - 200b + d^2) / (200d - 2bd) = (200b - 10000 + d^2) / (2bd)
Cross multiplying, we get:
(10000 - 200b + d^2)(2bd) = (200b - 10000 + d^2)(200d - 2bd)
Expanding both sides:
20000bd - 400b^2 + 2bd^2 = 40000d - 400bd + 200b^2 - 200000 + 200d^2 - 200bd
Rearranging the terms:
2bd^2 + 200b^2 + 200bd + 200000 + 400bd + 200000 - 20000bd + 40000d - 200d^2 = 0
Rearranging and simplifying further:
-2bd^2 + 200b^2 + 400bd + 40000d - 200d^2 = -400000
Now we can simplify by dividing everything by 2 to get:
-bd^2 + 100b^2 + 200bd + 20000d - 100d^2 = -200000
We have now extracted a single equation relating b and d. However, there may be multiple solutions to this equation, so it is a non-linear system and may require further analysis or the use of numerical methods to find the exact values of b and d.
cos(145) = (10000 - 200b + d^2) / (200d - 2bd)
cos(225) = (200b - 10000 + d^2) / (2bd)
Solve simultaneously
1 answer
1 answer