Chapter 9: Q. 9.66 (page 904)

Solve :- $x^{\frac{1}{2}} + 8 x^{\frac{1}{4}} + 15 = 0$

Short Answer

Expert verified

Solution for equation will be -

$x = 625$
$x = 81$

Step by step solution

Step 1. Given Data

Quadratic Equation - $x^{\frac{1}{2}} + 8 x^{\frac{1}{4}} + 15 = 0$

Step 2. To Find

We have to solve it and find the value of x.

Step 3. Explanation

Let the value of $x^{\frac{1}{4}} = u$

Then the equation is -

$x^{\frac{1}{2}} + 8 x^{\frac{1}{4}} + 15 = 0$

${(x^{\frac{1}{4}})}^{2} + 8 x^{\frac{1}{4}} + 15 = 0$

Put the value of $x^{\frac{1}{4}} = u$

$u^{2} + 8 u + 15 = 0$

$(u + 5) (u + 3) = 0$

By using zero product property -

$u + 5 = 0$ , $u + 3 = 0$

role="math" localid="1645027263305" $u = (- 5)$ , role="math" localid="1645027241340" $u = (- 3)$

Step 4. Calculation

Replace u with $x^{\frac{1}{4}}$

$x^{\frac{1}{4}} = (- 5)$ , $x^{\frac{1}{4}} = (- 3)$

Solve for x by do power fourth both sides

${(x^{\frac{1}{4}})}^{4} = {(- 5)}^{4}$ , ${(x^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

$x = 624$ , $x = 81$

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Solve :- $x^{\frac{1}{2}} + 8 x^{\frac{1}{4}} + 15 = 0$

Short Answer

Step by step solution

Step 1. Given Data

Step 2. To Find

Step 3. Explanation

Step 4. Calculation

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Solve :- x12+8x14+15=0

Short Answer

Step by step solution

Step 1. Given Data

Step 2. To Find

Step 3. Explanation

Step 4. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Solve :- $x^{\frac{1}{2}} + 8 x^{\frac{1}{4}} + 15 = 0$