Simplify (4 √ 14 + 4 √ 10 ) ( 3 √ 7 − 4 √ 5 )

Mathematics

1 answer:

Iteru [2.4K]3 years ago

4 0

Answer:

4 sqrt(2) - sqrt(70)

Step-by-step explanation:

Simplify the following:

(4 sqrt(14) + 4 sqrt(10)) (3 sqrt(7) - 4 sqrt(5))

Factor 4 out of 4 sqrt(14) + 4 sqrt(10) giving 4 (sqrt(14) + sqrt(10)):

4 (sqrt(14) + sqrt(10)) (3 sqrt(7) - 4 sqrt(5))

(sqrt(10) + sqrt(14)) (3 sqrt(7) - 4 sqrt(5)) = sqrt(10) (-4 sqrt(5)) + sqrt(10)×3 sqrt(7) + sqrt(14) (-4 sqrt(5)) + sqrt(14)×3 sqrt(7) = -20 sqrt(2) + 3 sqrt(70) - 4 sqrt(70) + 21 sqrt(2) = sqrt(2) - sqrt(70):

Answer: 4 sqrt(2) - sqrt(70)

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LUCKY_DIMON [66]

Since BD bisects angle ABC, that means angle ABD and angle CBD are equal to each other. With that set up the equation to solve for x like this:

-4x+33 = 2x+81
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x = -8

Now substitute that to ABD
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here’s CBD
2(-8) + 81
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=65

Finally angle ABC will be double the amount of ABD or CBD so 65 times 2 is 130.

ANSWERS: (angles)
ABD and CBD: 65
ABC: 130

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