From the question, the distance between p and r, by Pythagoras, is √x2+9 and the distance between r and q is √[5−x]2+16.
So the total cost C is will be 2[√x2+9]2 +3[√[5−x2]+16]2, this because the question tell us that the cost is dependent on the ' square' of the distance, and the 'square' of square root of a function is just the function. e.g, [√a]2=a.
Thus we have C =2[x2+9] + 3[[5−x]2+16] and expanding the brackets in the expression,
C =2x2+18+ 3[25−10x+x2+16],
=2x2+18+75−30x+3x2+48, and collecting like terms gives the expression in the question. Hope this helps.
