Maths Question:
$\begin{align} & \text{The sum of three numbers in A}\text{.P is 18 and the sum of theirs square } \\ & \text{is 206}\text{. Find the numbers} \\\end{align}$
Maths Solution:
$\begin{align} & \text{Let the AP be }(a-d),d,(a+d) \\ & \text{Sum of the A}\text{.P}=(a-d)+d+(a+d)=3a=18 \\ & a=6 \\ & \text{Product of the A}\text{.P}={{(a-d)}^{2}}+{{a}^{2}}+{{(a+d)}^{2}}=108 \\ & {{a}^{2}}-2ad+{{d}^{2}}+{{a}^{2}}+{{a}^{2}}+2ad+{{d}^{2}}=206 \\ & 3{{a}^{2}}+2{{d}^{2}}=206----(i) \\ & \text{3(6}{{\text{)}}^{2}}+2{{d}^{2}}=206 \\ & 108+2{{d}^{2}}=206 \\ & 2{{d}^{2}}=98,\text{ }{{d}^{2}}=49,\text{ }d=\pm 7 \\\end{align}$
University mathstopic: