Help rn please!! I’ll mark as brainliest for the first person to answer

Anybody help me to solve this question.

Mumz [18]

Answer:

$\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)} are\ in\ AP$

Step-by-step explanation:

Given that $(b-c)^2, (c-a)^2 , (a-b)^2$ are in AP

To prove: $\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)}$ are in AP

From given as we know if p , q, r are in AP then 2q= p+r.

$2(c-a)^2= (b-c)^2+(a-b)^2\\\\\Rightarrow 2(c^2+a^2-2ac)=b^2+c^2-2bc+a^2+b^2-2ab\\\\\Rightarrow 2c^2+2a^2-4ac= 2b^2+c^2+a^2 -2bc-2ab\\\\\Rightarrow a^2+c^2-2b^2-4ac= -2bc-2ab\\\\\Rightarrow a^2-2b^2+c^2= 4ac-2bc-2ab$

Now

$\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)}2\dfrac{1}{(c-a)} =\dfrac{1}{(b-c)}+\dfrac{1}{(a-b)}\\\\\Rightarrow \dfrac{2}{(c-a)}= \dfrac{a-b+b-c}{(b-c)(a-b)} \\\\\Rightarrow \dfrac{2}{(c-a)}= \dfrac{a-c}{(b-c)(a-b)} \\\\\Rightarrow2(b-c)(a-b) = (c-a)(a-c) \\\\\Rightarrow 2(ab-b^2-ac+bc)= -(a-c)^2\\\\\Rightarrow 2ab- 2b^2-2ac+2bc = -a^2-c^2+2ac\\\\\Rightarrow a^2-2b^2+c^2=4ac-2ab-2bc$

Which is the result of AP

.

Hence proved

6 0

3 years ago

(-1,4) and ( 1, -1) Find the distance between each pair of points

Nikolay [14]

Answer:

$\sqrt{29}$

Step-by-step explanation:

We are basically trying to find the hypotenuse of the triangle.

The distance between the x is 2, and the distance between the y is 5, which makes a length and a width.

Pythagrenum theorem: a^2+b^2=c^2

2^2 is 4, 5^2 is 25.

4+25 is 29.

The distance is $\sqrt{29}$ .

8 0

3 years ago

How do you calculate the value of the height, base or width of a rectangle, when the given volume, is 10m^3 and the base is twic

harkovskaia [24]

The length and width of the rectangle is 2√5m and √5m respectively

<h3>Volume of a rectangle</h3>

The formula for calculating the volume of a rectangle is expressed as:

V = lw

where

l is the length

w is the width

h is the height

If base is twice its width, then l = 2w

Substitute

10 = w(2w)

10 = 2w²

5 = w²

w = √5 m

Since l = 2w

l = 2√5m

Hence the length and width of the rectangle is 2√5m and √5m respectively

Learn more on volume of rectangle here: brainly.com/question/4062480

#SPJ1

3 0

2 years ago

In May, Liam and Charlie had the same amount of money in their savings accounts. In June, Liam deposited $140 into his account.

NeX [460]

I Think The Answer Is 2940

4 0

4 years ago

F(x) = x^2 + 8x + 15; Find f(-14/5)

mamaluj [8]

Answer:

either 449/25 or 11/25 depends on the -14/5 or

Step-by-step explanation:

$- \frac{14}{25} or \: \frac{ - 14}{25}$

if it the first one then the answer should be 449/25 but if ut the second one it should be 11/25 .

u just substitute the -14/5 to x then solve

7 0

2 years ago