Question

|x^2+6x+6 |= | x^2+4x+9 |+ | 2x - 3 |​ ,,,,, find the least positive integer satisfying the given equation ...

Answer 1

Answer:

2

Step-by-step explanation:

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Answer 2

Answer: No such integer exists

Step-by-step explanation:

• Given: $|x^{2} +6x+6|=|x^{2} +4x+9|+|2x-3|$
• To find: The least positive integer which satisfies the given equation.
• Concept: If any term comes out of modulus it becomes positive and the solving Quadratic equation.
• Solution:

        According to question,

          $|x^{2} +6x+6|=|x^{2} +4x+9|+|2x-3|$

      ⇒$x^{2} +6x+6=x^{2} +4x+9-2x+3$

      ⇒$4x=6$

      ⇒$x=\frac{3}{2}$

Now again,

         $|x^{2} +6x+6|=|x^{2} +4x+9|+|2x-3|$

     ⇒$x^{2} +6x+6=-x^{2} -4x-9+2x-3$

     ⇒$2x^{2} +8x+18=0$

     ⇒$x^{2} +4x+9=0$

     ⇒x= −2+2.23607i and x= −2−2.23607i

Again,

      $|x^{2} +6x+6|=|x^{2} +4x+9|+|2x-3|$

  ⇒$-x^{2} -6x-6=x^{2} +4x+9+2x-3$

  ⇒$2x^{2} +12x+12=0$

  ⇒$x^{2} +6x+6=0$

  ⇒ x=−1.26795 and x=−4.73205

So, after looking at the solutions we can say that no such positive integer exists in this case.

• Hence, there exists no positive integer which satisfies the given equation.

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