Question

If 10 + x, x + 4x + 1 are in GP then find x. ​

Answer 1

Answer:

this is a hard one but I will try

Step-by-step explanation:

Given that (2x-1),(4x-1) and (7+2x) are in G.P

In that case, the ratio between any two consecutive terms

must be a constant

⇒

2x−1

4x−1

=

4x−1

7+2x

⇒(4x−1)

2

=(7+2x)(2x−1)

⇒16x

2

−8x+1=4x

2

+12x−7

⇒12x

2

−20x+8=0

Dividing the above equation by 4 on both sides of the equality we get

⇒3x

2

−5x+2=0

⇒3x

2

−3x−2x+2=0

⇒3x(x−1)−2(x−1)=0

∴x=2/3 or x=1

For x=1/3

the three terms will be :

3

1

,

3

5

,

3

25

,....

the common ratio of the above GP is 5

∴ the next term i.e. 4th term will be :

3

25×5

=125/3

For x=1

the three terms will be : 1,3,9,...

the common ratio is 3

∴ the next term i.e. 4th term will be 9×3=27

Answer 2

SOLUTION

GIVEN

10 + x , x + 4 , x + 1 are in GP

TO DETERMINE

The value of x

EVALUATION

Here it is given that 10 + x , x + 4 , x + 1 are in GP

So by the given condition

$\sf{ {(x + 4)}^{2} = (10 + x)(x + 1)}$

$\sf{ \implies {x}^{2} + 8x + 16 = 10x + 10 + {x}^{2} + x}$

$\sf{ \implies {x}^{2} + 8x + 16 = {x}^{2} + 11x + 10 }$

$\sf{ \implies 8x - 11x = 10 - 16}$

$\sf{ \implies - 3x = - 6}$

$\sf{ \implies x = 2}$

FINAL ANSWER

Hence the required value of x = 2

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