Chapter 9: Q. 9.167 (page 1102)

Try It.
Solve: $\sqrt{y - 3} + 2 = \sqrt{4 y + 2}$

Short Answer

Expert verified

Ans: $\sqrt{y - 3} + 2 = \sqrt{4 y + 2} \Rightarrow y = \frac{5 + 4 \sqrt{26} i}{9}, \frac{5 + 4 \sqrt{26} i}{9} (I M A G I N A R Y R O O T S)$

Step by step solution

Step 1. Given information.

given expression $\sqrt{y - 3} + 2 = \sqrt{4 y + 2}$

Step 2. Square both sides of the equation and solve it.

${(\sqrt{y - 3} + 2)}^{2} = {(\sqrt{4 y + 2})}^{2} \Rightarrow y - 3 + 4 + 4 \sqrt{y - 3} = 4 y + 2 \Rightarrow 4 \sqrt{y - 3} = 3 y + 1$

Again, square both sides of the equation and solve it.

${(4 \sqrt{y - 3})}^{2} = {(3 y + 1)}^{2} \Rightarrow 16 (y - 3) = 9 y^{2} + 1 + 6 y \Rightarrow 16 y - 48 = 9 y^{2} + 1 + 6 y \Rightarrow 9 y^{2} - 10 y + 49 = 0$

Step 4. Find Discriminant of the equation 9y2-10y+49 =0

Since, Discriminant $D = b^{2} - 4 a c$

here $a = 9, b = - 10, c = 49$

$D = - 10^{2} - 4 \times 9 \times 49 = - 1664$

since Discriminant is negative the roots will be imaginary.

Step 5. Then the value of y.

$y = \frac{- b + \sqrt{D}}{2 a}, \frac{- b - \sqrt{D}}{2 a} \Rightarrow y = \frac{- (- 10) + \sqrt{- 1664}}{2 \times 9}, \frac{- (- 10) - \sqrt{- 1664}}{2 \times 9} \Rightarrow y = \frac{5 + 4 \sqrt{26} i}{9}, \frac{5 + 4 \sqrt{26} i}{9}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Try It.
Solve: $\sqrt{y - 3} + 2 = \sqrt{4 y + 2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Square both sides of the equation and solve it.

Again, square both sides of the equation and solve it.

Step 4. Find Discriminant of the equation 9y2-10y+49 =0

Step 5. Then the value of y.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Logic and Functions

Discrete Mathematics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Try It.Solve: y−3+2=4y+2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Square both sides of the equation and solve it.

Again, square both sides of the equation and solve it.

Step 4. Find Discriminant of the equation 9y2-10y+49 =0

Step 5. Then the value of y.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Logic and Functions

Discrete Mathematics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Try It.
Solve: $\sqrt{y - 3} + 2 = \sqrt{4 y + 2}$