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 - ( a , b ) , t h e n a 2 + b 2 is equal to_____. [2026]

Question

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 $ℝ - (a, b), then a^{2} + b^{2}$ is equal to_____. [2026]

Smart Achievers · Accepted Answer

(90)

$Let first three terms of G.P. are \frac{A}{r}, A, A r$

$\frac{A}{r} \cdot A \cdot A r = 27$

$A^{3} = 27 \Rightarrow A = 3$

$3 (\frac{1}{r} + 1 + r) = 3 + 3 (r + \frac{1}{r})$

$We know, r + \frac{1}{r} \geq 2 or r + \frac{1}{r} \leq - 2$

$S \in ℝ - (- 3, 9)$

$a^{2} + b^{2} = 9 + 81 = 90$

Solution

Q.
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 $ℝ - (a, b), then a^{2} + b^{2}$ is equal to_____. [2026]

Want Us to Email you About Special Offers & Updates?

Solution

Q. 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 ℝ-(a,b), then a2+b2 is equal to_____. [2026]

Ans. (90) Let first three terms of G.P. are Ar, A, Ar Ar·A·Ar=27 A3=27⇒A=3 3(1r+1+r)=3+3(r+1r) We know, r+1r≥2 or r+1r≤-2 S∈ℝ-(-3,9) a2+b2=9+81=90

Want Us to Email you About Special Offers & Updates?

Q.
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 $ℝ - (a, b), then a^{2} + b^{2}$ is equal to_____. [2026]