Q. 8.115 Solve:聽x聽鈭捖�2聽+聽2聽=聽x.... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.115 (page 814)

Solve: $\sqrt{x 鈭� 2} + 2 = x .$

Short Answer

Expert verified

The solutions are, $x = 3$ and $x = 2$ .

Step by step solution

Step 1 Given equation is,

$\sqrt{x 鈭� 2} + 2 = x .$

The product of binomial squares pattern is given by,

${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$

The objective is, we need to find the solution for the given equation.

To isolate the radical, subtract $2$ on both sides.

$\sqrt{x 鈭� 2} + 2 - 2 = x - 2 \sqrt{x 鈭� 2} = x - 2$

Step 2 Now square on both sides.

$x - 2 = {(x - 2)}^{2}$

Now use the product of binomial squares pattern on the right side.

$x - 2 = x^{2} - 2 (x) (2) + {(2)}^{2} x - 2 = x^{2} - 4 x + 4$

Now simplify the obtained equation.

$x - 2 = x^{2} - 4 x + 4 x^{2} - 4 x + 4 - x + 2 = 0 x^{2} - 5 x + 6 = 0$

Now factorize the obtained equation.

$(x - 3) (x - 2) = 0$

Now use the zero product property.

$x - 3 = 0 x = 3 x - 2 = 0 x = 2$

Step 3 Let us check the answer.

Substitute $x = 3$ into the equation.

$\sqrt{3 鈭� 2} + 2 = 3 \sqrt{1} + 2 = 3 1 + 2 = 3 3 = 3$

which is true.

Substitute $x = 2$ into the equation $\sqrt{x 鈭� 2} + 2 = x$ .

$\sqrt{2 鈭� 2} + 2 = 2 \sqrt{0} + 2 = 2 0 + 2 = 2 2 = 2$

which is true.

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91影视

Solve: $\sqrt{x 鈭� 2} + 2 = x .$

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 Now square on both sides.

Step 3 Let us check the answer.

One App. One Place for Learning.

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91影视

Solve:x鈭�2+2=x.

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 Now square on both sides.

Step 3 Let us check the answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve: $\sqrt{x 鈭� 2} + 2 = x .$