$$ ext{ যদি }\left|\begin{array}{ccc}1 & 1 & 1 \x & a & b \x^2 & a^2 & b^2\end{array} ight|=0 ext{ হলে, } x= ext{ ? }$$

Question

$$	ext{ যদি }\left|\begin{array}{ccc}1 & 1 & 1 \x & a & b \x^2 & a^2 & b^2\end{array}ight|=0 	ext{ হলে, } x=	ext{ ? }$$

Accepted Answer

$$\left|\begin{array}{ccc}1 & 1 & 1 \x & a & b \x^2 & a^2 & b^2\end{array}\right|=0 \Rightarrow\left|\begin{array}{ccc}0 & 0 & 1 \x-a & a-b & b \x^2-a^2 & a^2-b^2 & b^2\end{array}\right|=0$$ $$\begin{aligned}& \Rightarrow\left|\begin{array}{cc}\mathrm{x}-\mathrm{a} & \mathrm{a}-\mathrm{b} \(\mathrm{x}+\mathrm{a})(\mathrm{x}-\mathrm{a}) & (\mathrm{a}+\mathrm{b})(\mathrm{a}-\mathrm{b})\end{aligned}\right|=0 \& \Rightarrow(\mathrm{x}-\mathrm{a})(\mathrm{a}-\mathrm{b})\left|\begin{array}{cc}1 & 1 \\mathrm{x}+\mathrm{a} & \mathrm{a}+\mathrm{b}\end{array}\right|=0 \& \Rightarrow(\mathrm{x}-\mathrm{a})(\mathrm{a}-\mathrm{b})(\mathrm{a}+\mathrm{b}-\mathrm{x}-\mathrm{a})=0 \& \Rightarrow(\mathrm{x}-\mathrm{a})(\mathrm{a}-\mathrm{b})(\mathrm{b}-\mathrm{x})=0[\mathrm{a}-\mathrm{b} \neq 0] \therefore \mathrm{x} \& =\mathrm{a}, \mathrm{~b}\end{aligned}$$

Admission DU A প্রশ্নব্যাংক MCQ — \[\text { যদি }\left|\begin{array}{ccc}1 &amp; 1 &amp; 1 \\x &amp; a &am

আরো প্রশ্ন দেখো

Admission DU A প্রশ্নব্যাংক MCQ — \[\text { যদি }\left|\begin{array}{ccc}1 & 1 & 1 \\x & a &am