JEE Mains · Maths · STD 11 - 8. sequence and series
In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is \(\mathbb{R}-(a,b)\), then \(a^{2}+b^{2}\) is equal to ___ .
- A 80
- B 90
- C 100
- D 110
Answer & Solution
Correct Answer
(B) 90
Step-by-step Solution
Detailed explanation
Let first three terms of G.P. are \(\frac{\mathrm{A}}{\mathrm{r}}, \mathrm{A}, \mathrm{Ar}\) \(\frac{\mathrm{A}}{\mathrm{r}} \cdot \mathrm{A} \cdot \mathrm{Ar}=27\) \(A=3\) \(3\left(\frac{1}{r}+1+r\right)=3+3\left(r+\frac{1}{r}\right)\) We know, \(r+\frac{1}{r} \geq 2\) or…
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