Chapter 11: Q. 9.37 TI (page 1069)

Solve by completing the square :
$3 r^{2} - 2 r = 21$

Short Answer

Expert verified

The required value of $r$ is $3, \frac{- 7}{3}$

Step by step solution

Given information

$3 r^{2} - 2 r = 21$

Calculation

$3 r^{2} - 2 r = 21 \Rightarrow \frac{3 r^{2} - 2 r}{3} = \frac{21}{3} + \frac{1}{9} \Rightarrow r^{2} - \frac{2}{3} r = 7 \Rightarrow r^{2} - \frac{2}{3} r + (\frac{1}{2} \times {(- \frac{2}{3}))}^{2} = 7 \Rightarrow r^{2} - \frac{2}{3} r + \frac{1}{9} = 7 + \frac{1}{9} \Rightarrow {(r - \frac{1}{3})}^{2} = \frac{64}{9} \Rightarrow r - \frac{1}{3} = \pm \sqrt{\frac{64}{9}} \Rightarrow r = \frac{1}{3} \pm \sqrt{\frac{64}{9}} = \frac{1}{3} \pm \frac{8}{3} = \frac{1 + 8}{3}, \frac{1 - 8}{3} = \frac{9}{3}, \frac{- 7}{3} = 3, \frac{- 7}{3}$

The required value of $r$ is $3, \frac{- 7}{3}$

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Solve by completing the square :
$3 r^{2} - 2 r = 21$

Short Answer

Step by step solution

Given information

Calculation

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Solve by completing the square :3r2-2r=21

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Mechanics Maths

Calculus

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Solve by completing the square :
$3 r^{2} - 2 r = 21$