evaluation

• Aug 7th 2009, 12:28 PM
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?
• Aug 7th 2009, 12:39 PM
Amer
Quote:

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

$-2-4(-7)^2=-198$
• Aug 7th 2009, 12:42 PM
So are you saying there are two answers?
• Aug 7th 2009, 12:44 PM
Amer
Quote:

So are you saying there are two answers?

yeah
• Aug 7th 2009, 12:45 PM
Ok so i'm not sure what to do now then?
• Aug 7th 2009, 12:52 PM
Amer
Quote:

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

$-2-4(49)=-2-196=-198$
• Aug 7th 2009, 01:07 PM
Does the same apply to this formula

$a = -7, b = 4$

$a - b(a + b)$

$(-7) - 4((-7)+4) = 5$
• Aug 7th 2009, 01:10 PM
Amer
Quote:

Does the same apply to this formula

$a = -7, b = 4$

$a - b(a + b)$

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

it is correct
• Aug 7th 2009, 01:20 PM
stapel
Quote:

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)