Maharashtra BoardEnglish MediumSTD 9MathsAlgebraic Identities1 Mark
MCQ
If $\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}=1,$ then $a^3 + b^3 =$
A
$1$
B
$-1$
C
$\frac{1}{2}$
✓
$0$
✓
Answer
Correct option: D.
$0$
$\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}=1\Rightarrow\text{a}^2+\text{b}^2-\text{ab}=0$
Now by identity $a^3 + b^3 = (a + b)(a^2 + b^2 - ab).$
if $a^2 + b^2 - ab = 0.$
then $a^3 + b^3 = 0$
Hence, correct option is $(d).$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.