JEE Mains · Maths · STD 11 - 8. sequence and series
Suppose a, b, c are in A.P. and \( a^{2}, 2b^{2}, c^{2} \) are in G.P. If \( a < b < c \) and \( a+b+c=1, \) then \( 9(a^{2}+b^{2}+c^{2}) \) is equal to ___ .
- A 7
- B 9
- C 12
- D 15
Answer & Solution
Correct Answer
(B) 9
Step-by-step Solution
Detailed explanation
\(a = b - d , c = b + d , \Rightarrow b =\frac{1}{3}\) \(\Rightarrow 4 b^4=a^2 c^2\) \(\Rightarrow 4 b^4=[(b-d)(b+d)]^2\) \(\Rightarrow \frac{4}{81}=\left(\frac{1}{9}- d ^2\right)^2\) \(\Rightarrow\left(\frac{1}{9}- d ^2\right)= \pm \frac{2}{9}\)…
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