MCQ
If a + b = 8 and ab = 12 then $a^3+b^3=$
- A244
- ✓224
- C144
- D284
✓
Answer
Correct option: B.
224
(b)
We have, a + b = 8 and ab = 12
Now, $\quad a+b=8 \Rightarrow(a+b)^2=64 \Rightarrow a^2+b^2+2 a b=64 \Rightarrow a^2+b^2+2 \times 12=64 \Rightarrow a^2+b^2=40$ $ \therefore \quad a^3+b^3=(a+b)\left(a^2-a b+b^2\right)=8(40-12)=8 \times 28=224 $
We have, a + b = 8 and ab = 12
Now, $\quad a+b=8 \Rightarrow(a+b)^2=64 \Rightarrow a^2+b^2+2 a b=64 \Rightarrow a^2+b^2+2 \times 12=64 \Rightarrow a^2+b^2=40$ $ \therefore \quad a^3+b^3=(a+b)\left(a^2-a b+b^2\right)=8(40-12)=8 \times 28=224 $
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