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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

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BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

Suppose that your friend solved the equation ( x + 3 ) 2 = 25 as follows:

( x + 3 ) 2 = 25 x 2 + 6 x + 9 = 25 x 2 + 6 x 16 = 0 ( x + 8 ) ( x 2 ) = 0 x + 8 = 0        or        x 2 = 0 x = 8       or            x = 2

Is this a correct approach to the problem? Would you offer any suggestion about an easier approach to the problem?

To determine

To check:

The given method to solve the equation and also give other easy method to solve given equation.

Explanation

Formula used:

For any real number a,

x2=a

If and only if x=a or x=a.

Given:

The given method to solve the equation is,

(x+3)2=25x2+6x+9=25x2+6x16=0

Further on using the property ab=0 if and only if a=0 or b=0 the factors are as,

(x+8)(x2)=0x+8=0       or       x2=0x=8      or           x=2

Calculation:

The easier approach to the given problem is obtained by using the above mentioned property

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