Find x so that, x²+3x+1,x^2 +5x + 16 and x2 -7x + 3 are the consecutive terms of AP About the author Katherine
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. ━━━━━━━━━━━━━━━━━━━━━━ Reply
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. Reply
Solution –
Firstly, we have three equations
⠀
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,
⠀
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,
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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;
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.