Using the properties of proportion, solve the following equation for x.
x3+3x3x2+1=34191 [3 Marks]
Applying componendo and dividendo, we get;
x3+3x+3x2+1x3+3x−3x2−1=341+91341−91 (0.5 Marks)
⇒(x+1)3(x−1)3=432250 [(a+b)3=a3+b3+3ab(a+b)] (0.5 Marks)
⇒(x+1)3(x−1)3=216125=(65)3 (0.5 Marks)
⇒x+1x−1=65 (0.5 Marks)
Again, appplying componendo and dividendo we get:
x+1+x−1x+1−x+1=6+56−5
⇒2x2=111⇒x=11 (1 Mark)