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#### need solution for RD Sharma maths class 12 chapter 5 Determinants exercise Fill in the blanks question 23

Hint: Here, we use basic concept of determinant.

Given: $\left[\begin{array}{lll} (1+x)^{17} & (1+x)^{19} & (1+x)^{23} \\ (1+x)^{23} & (1+x)^{24} & (1+x)^{34} \\ (1+x)^{41} & (1+x)^{43} & (1+x)^{47} \end{array}\right]$

$A+B x+c x^{2}+\ldots \ldots \ldots \text { then find } A=?$

Solution: Let’s take something common from 3 rows

$(1+x)^{17}\left(1+x^{23}\right)\left(1+x^{41}\right)\left[\begin{array}{ccc} 1 & (1+x)^{2} & (1+x)^{6} \\ 1 & (1+x)^{6} & (1+x)^{11} \\ 1 & (1+x)^{2} & (1+x)^{6} \end{array}\right]$

Here, we clearly see that 1st and 3rd row has same value

So, f(x) = 0

So, here x  = 0 and

\begin{aligned} &A+B x+C x^{2} \ldots \ldots \ldots .=0 \\ &S o, A=0 \end{aligned}