If x=1+2+3, then x44x34x2+16x=?


Answer:

8

Step by Step Explanation:
  1. Given: x=1+2+3
    According to the question, we need to find the value of x=1+2+3
  2. x=1+2+3x1=2+3
    Taking the square on both sides
    x2+12x=2+3+2×2×3     [ Using (a+b)2=a2+b2+2ab]x22x4=26
  3. Again, taking the square on both sides
    \begin{align} & \space x^4 + 4x^2 + 16 - 4x^3 + 16x - 8x^2 = 4 \times 6 \space\space\space\space\space [\because (a - b - c)^2 = a^2 + b^2 + c^2 -2ab + 2bc -2ca ] \\ & \implies x^4 - 4x^3 -4x^2 + 16x + 16 = 24 \\ & \implies x^4 - 4x^3 -4x^2 + 16x = 8 \\ \end{align}

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