Q12 PT. Solve the given equation and che... [FREE SOLUTION]

Chapter 10: Q12 PT. (page 661)

Solve the given equation and check the solution.
$\sqrt{4 x 鈭� 3} = 6 鈭� x$

Short Answer

Expert verified

The solution of $\sqrt{4 x 鈭� 3} = 6 鈭� x$ is 3.

Step by step solution

Step 1. State the concept of ‘square of a square root’.

When the square root of a term is squared, then the resulting value will be the term which is inside the root. That is,

${(\sqrt{a})}^{2} = a$

Step 2. State the concept of ‘quadratic equation’.

The equation which consists of only one variable and whose highest degree is 鈥�2鈥�, is called as quadratic equation.

Step 3. Define ‘Factorization method’.

The method of writing polynomials into its simplest form, that is writing it as the product of factors is called as factorization method.

Step 4. Find the value of ‘x’.

Solve the equation $\sqrt{4 x 鈭� 3} = 6 鈭� x$ to get the value of 鈥�x鈥�.

$\sqrt{4 x 鈭� 3} = 6 鈭� x$

Squaring both the sides

${(\sqrt{4 x 鈭� 3})}^{2} = {(6 鈭� x)}^{2} 4 x 鈭� 3 = {(6)}^{2} 鈭� 2 (6) (x) + {(x)}^{2} 鈥夆赌夆赌夆赌夆赌� [Using {(\sqrt{a})}^{2} = a 鈥夆赌塧苍诲鈥夆赌� {(a 鈭� b)}^{2} = a^{2} 鈭� 2 a b + b^{2} 鈥�] 4 x 鈭� 3 = 36 鈭� 12 x + x^{2} 4 x 鈭� 3 = x^{2} 鈭� 12 x + 36 x^{2} 鈭� 12 x + 36 = 4 x 鈭� 3 x^{2} 鈭� 12 x + 36 鈭� 4 x + 3 = 0 x^{2} 鈭� 12 x 鈭� 4 x + 36 + 3 = 0 x^{2} 鈭� 16 x + 39 = 0 x^{2} 鈭� 13 x 鈭� 3 x + 39 = 0 鈥夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌� [鲍蝉颈苍驳鈥夆赌塮补肠迟辞谤颈锄补迟颈辞苍鈥夆赌尘别迟丑辞诲] x (x 鈭� 13) 鈭� 3 (x 鈭� 13) = 0 (x 鈭� 13) (x 鈭� 3) = 0$

$(x 鈭� 13) = 0 鈥夆赌夆赌夆赌夆赌夆€夆€塷r鈥夆赌夆赌夆赌夆赌夆€� (x 鈭� 3) = 0 鈥夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌� [滨蹿鈥夆赌� a b = 0, 鈥夆赌塼丑别苍鈥夆赌塭颈迟丑别谤鈥夆赌� a = 0 鈥夆赌塷谤鈥夆赌� b = 0] 鈥夆赌夆赌夆赌� x 鈭� 13 = 0 鈥夆赌夆赌夆赌夆赌夆€夆€塷r鈥夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌� x 鈭� 3 = 0 鈥夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌� x = 13 鈥夆赌夆赌夆赌夆赌塷r鈥夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€� x = 3$

Step 5. Verify the solution.

Consider $x = 13$

Substitute $x = 13$ in the left hand side(L.H.S) of the equation $\sqrt{4 x 鈭� 3} = 6 鈭� x$ .

$L.H.S = \sqrt{4 x 鈭� 3} = \sqrt{4 (13) 鈭� 3} = \sqrt{52 鈭� 3} = \sqrt{49} = 7 鈥夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆€夆€� 鈥� (1)$

Now, Substitute $x = 13$ in the right hand side(R.H.S) of the equation $\sqrt{4 x 鈭� 3} = 6 鈭� x$ .

$R.H.S = 6 鈭� x = 6 鈭� 13 = 鈭� 7 鈥夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌� 鈥� (2)$

From (1) and (2)

$L.H.S 鈮� R.H.S$

Thus, $x = 13$ does not satisfies the given equation.

Consider $x = 13$

Substitute $x = 13$ in the left hand side(L.H.S) of the equation $\sqrt{4 x 鈭� 3} = 6 鈭� x$ .

$L.H.S = \sqrt{4 x 鈭� 3} = \sqrt{4 (3) 鈭� 3} = \sqrt{12 鈭� 3} = \sqrt{9} = 3 鈥夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆€夆€� 鈥� (3)$

Now, Substitute $x = 3$ in the right hand side(R.H.S) of the equation $\sqrt{4 x 鈭� 3} = 6 鈭� x$ .

$R.H.S = 6 鈭� x = 6 鈭� 3 = 3 鈥夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌� 鈥� (4)$

From (3) and (4)

$L.H.S=R.H.S$

$x = 3$ satisfies the given equation.

Therefore, $x = 3$ is the solution of the given equation.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

91影视

Solve the given equation and check the solution.
$\sqrt{4 x 鈭� 3} = 6 鈭� x$

Short Answer

Step by step solution

Step 1. State the concept of ‘square of a square root’.

Step 2. State the concept of ‘quadratic equation’.

Step 3. Define ‘Factorization method’.

Step 4. Find the value of ‘x’.

Step 5. Verify the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Statistics

Geometry

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

91影视

Solve the given equation and check the solution.4x鈭�3=6鈭�x

Short Answer

Step by step solution

Step 1. State the concept of ‘square of a square root’.

Step 2. State the concept of ‘quadratic equation’.

Step 3. Define ‘Factorization method’.

Step 4. Find the value of ‘x’.

Step 5. Verify the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Statistics

Geometry

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve the given equation and check the solution.
$\sqrt{4 x 鈭� 3} = 6 鈭� x$