   Chapter 0.3, Problem 48E

Chapter
Section
Textbook Problem

In Exercises 31–48, (a) factor the given expression, and (b) set the expression equal to zero and solve for the unknown (x in the odd-numbered exercises and y in the even-numbered exercises.) y 4 + 2 y 2 − 3

(a)

To determine

To calculate: The factors of the expression y4+2y23.

Explanation

Given information:

The expression, y4+2y23.

Formula used:

Steps to calculate the factors of quadratic equation ax2+bx+c by trial and error method,

Step1: Factor ax2 as (a1x)(a2x) with a1 positive.

Step2: Factor c as c1c2.

Step 3: Check if ax2+bx+c=(a1x±c1)(a2x±c2)

If yes, then (a1x±c1)(a2x±c2) are the factors.

Step 4: If not, try other factorization of ax2 and c and repeat all the steps.

The distributive law,

(a±b)c=ac±bc

Where, a, b and c are any real numbers.

Difference of two squares,

a2b2=(a+b)(ab)

Where, a and b are the real numbers.

Calculation:

Consider the expression,

y4+2y23

Rewrite the above expression as,

(y2)2+2y23

Substitute y2=x in the above expression,

(x)2+2x3

Factor of x2 are (x)(x).

The factors of 3 are (1)(3),(1)(3),(3)(1)and(3)(1) .

Consider the factors (x)(x) and (1)(3)

(b)

To determine

To calculate: The value of y when the expression y4+2y23 is equal to zero.

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