Question

Solve:

72/z-3 + 72/z+3 = 10

Answer 1

If the expression on the LHS is (72/z) -3 + (72/z) +3 , then 144/z = 10 or, 10z = 144 so that z = 144/1`0= 72/5.

However, if the expression on the LHS is 72/(z-3) + 72/(z+3), then we have 72(z+3)+72(z-3)/( z-3)(z+3) = 10 or, 144z= 10(z² -9) or, 10z² -144z -90 = 0 or, 5z² -72z -45 = 0. Now, on using the quadratic formula, we have z = [72±?{ (-72)² -4*5*(-45)}]/2*5 = [72±?(5184+900)]/10 = (72±?6084)/10 = (72± 78)/10 . Thus, either z = (72-78)/10 = -6/10 = -3/5 or, z = (72+78)/10 = 150/10 = 15. The answer is, then, z-3/5 or, z = 15.