# evaluation

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• August 7th 2009, 11:28 AM
ADY
evaluation
when $c=-7$and $d=4$

$\sqrt{d} - dc^2$

$\sqrt{4} - 4 x (-7)^2$

$2 - 4 x (-7)^2 = -194$

this right?
• August 7th 2009, 11:39 AM
Amer
Quote:

Originally Posted by ADY
when $c=-7$and $d=4$

$\sqrt{d} - dc^2$

$\sqrt{4} - 4 x (-7)^2$

$2 - 4 x (-7)^2 = -194$

this right?

it is right but $\sqrt{4}=\mp 2$ since $2^2=4$ and $(-2)^2=4$ so you will have two answers the first one you find it
the second one

$-2-4(-7)^2=-198$
• August 7th 2009, 11:42 AM
ADY
So are you saying there are two answers?
• August 7th 2009, 11:44 AM
Amer
Quote:

Originally Posted by ADY
So are you saying there are two answers?

yeah
• August 7th 2009, 11:45 AM
ADY
Ok so i'm not sure what to do now then?
• August 7th 2009, 11:52 AM
Amer
Quote:

Originally Posted by ADY
Ok so i'm not sure what to do now then?

did you know that

$(-2)^2=4$
$(-4)^2=16$
$(-7)^2=49$

so

$\sqrt{4}=\mp 2$
$\sqrt{16}=\mp 4$
$\sqrt{49}=\mp 7$

in general
$\sqrt{a^2}=\mp a$ a is real number

in you question

$\sqrt{4}-4(-7)^2$ have two solutions since $\sqrt{4}=2$ and $\sqrt{4}=-2$

first one
$2-4(49)=2-196=-194$

second one

$-2-4(49)=-2-196=-198$
• August 7th 2009, 12:07 PM
ADY
Does the same apply to this formula

$a = -7, b = 4$

$a - b(a + b)$

$(-7) - 4((-7)+4) = 5$
• August 7th 2009, 12:10 PM
Amer
Quote:

Originally Posted by ADY
Does the same apply to this formula

$a = -7, b = 4$

$a - b(a + b)$

$(-7) - 4((-7)+4) = 5$

it is correct
• August 7th 2009, 12:20 PM
stapel
Quote:

Originally Posted by ADY
So are you saying there are two answers?

One might say that the evaluation has two answers, but this would be incorrect. (Blush)

While one solves "x^2 = 4" for the two solution values, -2 and +2, "the" value of the square root of 4, sqrt[4], is defined to be the principal (that is, the positive real) value: sqrt[4] = 2.

So no, there will most definitely not be two answers to this one evaluation exercise! (Surprised)

$\sqrt{d}\, -\, dc^2\, =\,\sqrt{4}\, -\, (4)(-7)^2$

. . . $=\, 2\, -\,4(49)\, =\, 2\, -\, 196\, =\, -194$

And the above is the only answer! (Wink)