Chapter 9: Q. 87E (page 885)

In the following exercises, solve the completing squares-
$u^{2} - 14 u + 12 = 1$

Short Answer

Expert verified

The solution is $\sqrt{38} + 7, - \sqrt{38} + 7$

Step by step solution

Step 1. Given information

The equation: $u^{2} - 14 u + 12 = 1$

Step 2. Calculation

Solving the equation,

$u^{2} - 14 u + 12 = 1$

$\Rightarrow u^{2} - 14 u = - 11$

$\Rightarrow u^{2} - 14 u + {[\frac{1}{2} \times (- 14)]}^{2} = - 11 + {[\frac{1}{2} \times (- 14)]}^{2}$

\Rightarrow u^{2} - 14 u + 49 = 38

$\Rightarrow u^{2} - 7 u - 7 u + 49 = 38$

$\Rightarrow u (u - 7) - 7 (u - 7) = 38$

role="math" localid="1645273024904" $\Rightarrow {(u - 7)}^{2} = 38 \Rightarrow u - 7 = \pm \sqrt{38}$

$\Rightarrow u = \pm \sqrt{38} + 7$

The required value of $u$ ,

$\sqrt{38} + 7, - \sqrt{38} + 7$

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In the following exercises, solve the completing squares-
$u^{2} - 14 u + 12 = 1$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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In the following exercises, solve the completing squares-u2-14u+12=1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Logic and Functions

Discrete Mathematics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the completing squares-
$u^{2} - 14 u + 12 = 1$