Question

4. Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, foi
1. Find the value of x for which ( 8x + 4), ( 6x - 2) and (2x + 7) are in A.P.
2. If x+1, 3r and 4x + 2 are in A.P., find the value of x.
3. Show that (a - b)2(a2 +b?) and (a + b)2 are in A.P.
numbers.​

Answer 1

Step-by-step explanation:

this is your answer.

a is 9 and d is 3

Answer 2

Question :

Find the value of x for which (8x+4),(6x−2) and (2x+7) are in A.P.

Answer :

If a,b,c are in A.P

b=a+c/2

According to question 8x+4,6x−2,2x+7 are in A.P

6x−2=(8x+4+2x+7)/2

6x−2=10x+11/2

2(6x−2)=10x+11

12x−4=10x+11

12x−10x=11+4

2x=15

x=15/2=7.5

Question :

If x+1,3x and 4x+2 are in A.P., find the value of x.

Answer :

Given

x+1,3x and 4x+2 are in A.P

then 3x−(x+1)=(4x+2)−3x [Common diff]

⇒2x−1=x+2

⇒x=3

Question :

Show that (a−b)²,(a² +b²) and (a+b)² are in AP.

Answer :

Assume that (a−b)² ,(a² +b²) and (a+b)² are in AP.

So, difference between two consecutive terms will be same.

(a² +b²)−(a−b)² =(a+b)² −(a² +b²)

(a² +b²)−(a² +b² −2ab)=a² +b² +2ab−a² −b²

2ab=2ab

Which is true.

Hence given terms are in AP.