જો left| begin{array}{ccc} a^2 & b^2 & c^2 ( | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) ધારો કે $\Delta = \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ (a + \lambda)^2 & (b + \lambda)^2 & (c + \lambda)^2 \ (a - \lambda)^2 & (b - \lamb

Vedclass · Accepted Answer

$4\lambda^2$

Vedclass · Answer

(C) ધારો કે $\Delta = \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ (a + \lambda)^2 & (b + \lambda)^2 & (c + \lambda)^2 \ (a - \lambda)^2 & (b - \lambda)^2 & (c - \lambda)^2 \end{array} ight|$.$R_2 	o R_2 - R_3$ પ્રક્રિયા કરતા:$\Delta = \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ (a + \lambda)^2 - (a - \lambda)^2 & (b + \lambda)^2 - (b - \lambda)^2 & (c + \lambda)^2 - (c - \lambda)^2 \ (a - \lambda)^2 & (b - \lambda)^2 & (c - \lambda)^2 \end{array} ight|$.$(x + y)^2 - (x - y)^2 = 4xy$ સૂત્રનો ઉપયોગ કરતા:$\Delta = \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ 4a\lambda & 4b\lambda & 4c\lambda \ (a - \lambda)^2 & (b - \lambda)^2 & (c - \lambda)^2 \end{array} ight|$.$R_2$ માંથી $4\lambda$ સામાન્ય લેતા:$\Delta = 4\lambda \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ a & b & c \ (a - \lambda)^2 & (b - \lambda)^2 & (c - \lambda)^2 \end{array} ight|$.$R_3 	o R_3 - R_1 + 2\lambda R_2$ પ્રક્રિયા કરતા:$(a - \lambda)^2 = a^2 + \lambda^2 - 2a\lambda$ હોવાથી,$R_3 - R_1 + 2\lambda R_2 = \lambda^2$ મળે છે:$\Delta = 4\lambda \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ a & b & c \ \lambda^2 & \lambda^2 & \lambda^2 \end{array} ight|$.$R_3$ માંથી $\lambda^2$ સામાન્ય લેતા:$\Delta = 4\lambda^3 \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ a & b & c \ 1 & 1 & 1 \end{array} ight|$.આપેલ સમીકરણ $k\lambda \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ a & b & c \ 1 & 1 & 1 \end{array} ight|$ સાથે સરખાવતા,$k\lambda = 4\lambda^3$ મળે,તેથી $k = 4\lambda^2$.

Similar Questions

નિશ્ચાયકનું મૂલ્ય શોધો: $\left| {\begin{array}{*{20}{c}}{{b^2} - ab}&{b - c}&{bc - ac}\\{ab - {a^2}}&{a - b}&{{b^2} - ab}\\{bc - ac}&{c - a}&{ab - {a^2}}\end{array}} \right|$

નિશ્ચાયક $\left|\begin{array}{ccc}a+b & a+2b & a+3b \\ a+2b & a+3b & a+4b \\ a+4b & a+5b & a+6b\end{array}\right|$ નું મૂલ્ય શોધો.

જો $a, b, c > 0$ અને $x, y, z \in R$ હોય,તો નિશ્ચાયક $\left| \begin{array}{ccc} (a^x + a^{-x})^2 & (a^x - a^{-x})^2 & 1 \\ (b^y + b^{-y})^2 & (b^y - b^{-y})^2 & 1 \\ (c^z + c^{-z})^2 & (c^z - c^{-z})^2 & 1 \end{array} \right|$ ની કિંમત શોધો.

$\left| {\begin{array}{ccc} 1/a & a^2 & bc \\ 1/b & b^2 & ca \\ 1/c & c^2 & ab \end{array}} \right| = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module