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Mathematics

1 answer:

Sedbober [7]3 years ago

6 0

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Solve for x.

Ivahew [28]

ANSWER

$x=\frac{2-\sqrt{10}} {3}$

or

$x=\frac{\sqrt{10}+2} {3}$

We have

$3x^2-4x-2=0$

Since we cannot factor easily, we complete the square.

Adding 2 to both sides give,

$3x^2-4x=2$

Dividing through by 3 gives

$x^2-\frac{4}{3}x= \frac{2}{3}$

Adding $(-\frac{2}{3})^2$ to both sides gives

$x^2-\frac{4}{3}x+(-\frac{2}{3})^2= \frac{2}{3}+(-\frac{2}{3})^2$

The expression on the Left Hand side is a perfect square.

$(x-\frac{2}{3})^2= \frac{2}{3}+\frac{4}{9}$

$\Rightarrow (x-\frac{2}{3})^2= \frac{10}{9}$

$\Rightarrow (x-\frac{2}{3})=\pm \sqrt{\frac{10}{9}}$

$\Rightarrow (x)=\frac{2}{3} \pm {\frac{\sqrt{10}}{3}$

Splitting the plus or minus sign gives

$x=\frac{2- \sqrt{10}} {3}$

or

$x=\frac{\sqrt{10}+2} {3}$

3 0

3 years ago

Read 2 more answers

3. A penny is made by combining 0.1 g of a copper alloy that costs $5.50 per kilogram (1000 grams) with

lbvjy [14]

.0001*5.5 + 1.5*x = 2
x=1.33 kg

6 0

3 years ago

Let a, b, c and x elements in the group G. In each of the following solve for x in terms of a, b, and c.

alina1380 [7]

Answer:

The answer is $x=a^{-1}cb^{-1}$ .

Step-by-step explanation:

First, it is important to recall that the group law is not commutative in general, so we cannot assume it here. In order to solve the exercise we need to remember the axioms of group, specially the existence of the inverse element, i.e., for each element $g\in G$ there exist another element, denoted by $g^{-1}$ such that $gg^{-1}=e$ , where $e$ stands for the identity element of G.