The geometric and harmonic means of two positive numbers x1 and x2 are 18 and 16 (8/13) respectively. The value of |x1-x2| is equal to

Question

The geometric and harmonic means of two positive numbers x1 and x2 are 18 and 16 (8/13) respectively. The value of |x1-x2| is equal to (A) 5 (B) 10 (C) 15 (D) 20

Tardigrade Admin · Accepted Answer

Θ x 1 x 2=324 text and (2 x 1 x 2/ x 1+ x 2)=(216/13) ⇒ x 1+ x 2=39 Θ(x1-x2)2=(x1+x2)2-4 x1 x2=(39)2-4 × 324=225 ⇒|x1-x2|=15 .

Q. The geometric and harmonic means of two positive numbers $x_{1}$ and $x_{2}$ are 18 and $16 \frac{8}{13}$ respectively. The value of $∣ x_{1} - x_{2} ∣$ is equal to

5

10

15

20

$Θ x_{1} x_{2} = 324$
$and \frac{2 x _{1} x _{2}}{x _{1} + x _{2}} = \frac{216}{13} \Rightarrow x_{1} + x_{2} = 39$
$Θ (x_{1} - x_{2})^{2} = (x_{1} + x_{2})^{2} - 4 x_{1} x_{2} = (39)^{2} - 4 \times 324 = 225$
$\Rightarrow ∣ x_{1} - x_{2} ∣ = 15.$

Q. The geometric and harmonic means of two positive numbers x1​ and x2​ are 18 and 16138​ respectively. The value of ∣x1​−x2​∣ is equal to

5

10

15

20

Θx1​x2​=324 and x1​+x2​2x1​x2​​=13216​⇒x1​+x2​=39 Θ(x1​−x2​)2=(x1​+x2​)2−4x1​x2​=(39)2−4×324=225 ⇒∣x1​−x2​∣=15.

Q. The geometric and harmonic means of two positive numbers $x_{1}$ and $x_{2}$ are 18 and $16 \frac{8}{13}$ respectively. The value of $∣ x_{1} - x_{2} ∣$ is equal to

$Θ x_{1} x_{2} = 324$
$and \frac{2 x _{1} x _{2}}{x _{1} + x _{2}} = \frac{216}{13} \Rightarrow x_{1} + x_{2} = 39$
$Θ (x_{1} - x_{2})^{2} = (x_{1} + x_{2})^{2} - 4 x_{1} x_{2} = (39)^{2} - 4 \times 324 = 225$
$\Rightarrow ∣ x_{1} - x_{2} ∣ = 15.$