History, 22.11.2019 10:31 lilmsnyah

What impact did invasions by viking and other groups have on europe?

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Answer from: rashawng2005

The Vikings launched an early attack on the monastery of Lindisfarne on a small island off the East coast of England. The monastery was plundered and burned, while monks were either killed or ensalved. Within ten years, the Vikings began attacks along the North coast of France. Charlemagne, king of the Franks, set up a series of defenses along the coast to ward off these Viking raids. In the late 700s, the Vikings invaded the British Isles, including areas of Ireland and Scotland. They established a settlement in Ireland, known as Dublin.

In 865 AD, a large army of Danish Vikings invaded England. Alfred the Great, King of England, defeated this Danish army in 878 and restricted the Danish Vikings to the eastern part of England, known as the Danelaw. Here people were subject to Danish law, rather than English law.

Answer from: chrisboykashifre1999

While the common consensus is that the impact of the Vikings during the Viking Age, which lasted from about 800 AD to 1100 AD, was not very enduring as the Vikings were skilled at assimilating into the local population, the Viking culture has had a lasting impact on the art, technology, society, and trade of every population they encountered. Not only does the concept of the Vikings have a firm hold in the Danish consciousness to this day, but Scandinavian traces are still apparent in the dialects of Scotland and Northern England today. The truth is that while they may have been viewed as barbarian raiders by popular culture until recent times, they were primarily skilled traders and explorers who opened up a host of new trade routes and discovered a number of new lands during their brief, but significant, reign as a prominent empire of early Europe.

Answer from: Quest

yes

explanation:

Answer from: Quest

answer

$x = \pm 2\sqrt{2} \: \: or \: \: x = \pm 1$

explanation

the given equation is

${x}^{4} - 9 {x}^{2} + 8 = 0$

we can rewrite this as:

$({x}^{2})^{2} - 9 {x}^{2} + 8 = 0$

let

$u = {x}^{2}$

then the equation becomes:

${u}^{2} - 9 {u}^{2} + 8 = 0$

the factors of 8 that sum up to -9 are {-1,-8}

we split the middle term with these factors to obtain,

${u}^{2} - u - 8u+ 8 = 0$

we factor by grouping to obtain:

$u(u - 1) - 8(u - 1) = 0$

$(u - 8)(u - 1) = 0$

apply the zero product property to get:

$u - 8 = 0 \: \: or \: \: u - 1 = 0$

$u = 8 \: or \: u = 1$

but

$u = {x}^{2}$

${x}^{2} = 8 \: or \: {x}^{2} = 1$

$x = \pm \sqrt{8} \: \: or \: \: x = \pm \: \sqrt{ 1}$

$x = \pm 2\sqrt{2} \: \: or \: \: x = \pm 1$

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