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Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248

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Chapter
Section
BuyFindarrow_forward

Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248
Textbook Problem

Solve the equations in Exercises 1–26.

x 4 x 2 = 6

To determine

To calculate: The solution of the equation x4x2=6.

Explanation

Given information:

The equation, x4x2=6.

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.

Zero product property,

If a product of two number is zero, one of the two must be zero.

Calculation:

Consider the expression,

x4x2=6

Rewrite the expression as,

x4x26=0

The left side expression is x4x26.

The above expression can be written as,

(x2)2x26

Substitute x2=y in the above expression,

y2y6

Factor of y2 are (y)(y).

The factors of 6 are (1)(6),(2)(3),(2)(3)and(1)(6).

Consider the factors (y)(y) and (1)(6).

Now,

(y+1)(y6)=y(y6)+1(y6)=y26y+y6=y25y6

Which is not the original expression

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