Question

Find x so that, x²+3x+1,x^2 +5x + 16 and x2 -7x + 3 are the consecutive terms of AP

Answer 1

Answer:-

Given:

x² + 3x + 1 , x² + 5x + 16 , x² - 7x + 3 are consecutive terms of an AP.

We know that;

If a , b , c are in AP then,

⟹ 2b = a + c

Let;

• a = x² + 3x + 1
• b = x² + 5x + 16
• c = x² - 7x + 3.

According to the question;

⟹ 2(x² + 5x + 16) = x² + 3x + 1 + x² - 7x + 3

⟹ 2x² + 10x + 32 = x² + x² + 3x - 7x + 1 + 3.

⟹ 2x² + 10x + 32 = 2x² - 4x + 4

⟹ 2x² + 10x - 2x² + 4x = 4 - 32

⟹ 14x = - 28

⟹ x = - 28/14

⟹ x = - 2

∴ The value of x is - 2.

Answer 2

Solution -

Firstly, we have three equations

• x² + 3x + 1
• x² + 5x + 16
• x² - 7x + 3

⠀

Now, we have to find the value of x so that these equations are the consecutive terms of A.P.

Since, in an A.P. a, b and c

⠀⠀⠀⠀⠀⠀❏ 2b = a + c

⠀

Consider,

• a = x² + 3x + 1
• b = x² + 5x + 16
• c = x² - 7x + 3

⠀

Substituting the values

→ 2(x² + 5x + 16) = x² + 3x + 1 + x² - 7x + 3

⠀

→ 2x² + 10x + 32 = 2x² - 4x + 4

⠀

Cancelling 2x² both the sides

→ 10x + 32 = -4x + 4

⠀

→ 10x + 4x = 4 - 32

⠀

→ 14x = -28

⠀

→ x = -28/14

⠀

→ x = -2

⠀

Hence,

• Required value of x is -2.

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