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Delvig [45]
3 years ago
14

If a + b + c.= 5 and ab + bc +ca = 10 , then prove that a3+ b3+ c3-3abc = -25

Mathematics
1 answer:
Alex Ar [27]3 years ago
3 0

Start with

(a+b+c)^3=a^3+b^3+c^3+3(a^2b+a^2c+ab^2+ac^2+b^2c+bc^2)+6abc

Given that a+b+c=5, we know (a+b+c)^3=125.

Also, ab+bc+ca=10, so

a^2b+a^2c+ab^2+ac^2+b^2c+bc^2=a(ab+ac)+b(ab+bc)+c(ac+bc)

=a(10-bc)+b(10-ca)+c(10-ab)

=10(a+b+c)-3abc

=50-3abc

So we have

125=a^3+b^3+c^3+3(50-3abc)+6abc

125=a^3+b^3+c^3+150-9abc+6abc

\implies -25=a^3+b^3+c^3-3abc

QED

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3 years ago
I need the answer to a parts I-iii and the answer to b
fomenos

Answer:

a)

i) Mean = 72

ii) Median = 72

iii) Mode = 72

b)

69, 70, 71, 72, 72, 72, 73, 74, 75

Step-by-step explanation:

<u>a. To find mean, median and mode</u>

It is given that all the 9 students get 72 marks.

Therefore the data set be,

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<u>i) mean </u>= (sum of data)/(total number of data)

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<u>ii) Median </u>- Central data in the data set when arranging ascending or descending order

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<u>iii) Mode </u>- Most repeating data in the data set

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<u>b). To find a data set</u>

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3 0
3 years ago
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Free_Kalibri [48]
Draw
Left side:
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Right side: (2)Circle=6
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5 0
3 years ago
PLEASE HELP ME SOLVE THIS Find all x-values for which f ( x ) = 2 for the function below.
alisha [4.7K]

Answer:

<h3>x = -3</h3>

Step-by-step explanation:

First let us get the equation of the coordinates

y-y0 = m(x-x0)

Using the coordinates ( - 3, 2 ), ( - 1, 0 )

m = 0-2/-1-(-3)

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Substitute m = -1 and (-1, 0) into the formula

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Since f(x) = 2

2 = -x-1

-x = 2+1

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x = -3

Hence the value of x is -3

3 0
3 years ago
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