Q. 9.167 Try It.Solve:聽聽y鈭�3+2=4y+2... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q. 9.167 (page 1102)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

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

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

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

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

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

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

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

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

$D = - 10^{2} - 4 脳 9 脳 49 = - 1664$

since Discriminant is negative the roots will be imaginary.

Step 5. Then the value of y.

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

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91影视

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

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.

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91影视

Try It.Solve: y鈭�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

Decision Maths

Mechanics Maths

Discrete Mathematics

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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