Let k_1, k_2 be the maximum and minimum | vedclass

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Question

For the system to be consistent $\Delta=0$

$\Rightarrow\left|\begin{array}{lll}{1} & {k} & {1} \ {k} & {1} & {2} \ {1} & {1}

Vedclass · Accepted Answer

$7$

Vedclass · Answer

For the system to be consistent $\Delta=0$

$\Rightarrow\left|\begin{array}{lll}{1} & {k} & {1} \ {k} & {1} & {2} \ {1} & {1} & {k}\end{array}ight|=0$

$\Rightarrow(k-1)\left(k^{2}+k-3ight)=0$

$\Rightarrow \mathrm{k}=1$ or $\mathrm{k}^{2}+\mathrm{k}-3=0$

But if $\mathrm{k}=1$ equations will have no solution

$\Rightarrow \mathrm{k}^{2}+\mathrm{k}=3$

Further if $\mathrm{k}^{2}+\mathrm{k}=3$ then none of the pair of lines are parallel

$\Rightarrow \mathrm{k}_{1}^{2}+\mathrm{k}_{2}^{2}=7$

Let $k_1$, $k_2$ be the maximum and minimum values of $k$ for which the system of equations given by

$x + ky = 1$ ; $kx + y = 2$; $x + y = k$ are consistent then $k_1^2 + k_2^2$ is equal to

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Let $k_1$, $k_2$ be the maximum and minimum values of $k$ for which the system of equations given by $x + ky = 1$ ; $kx + y = 2$; $x + y = k$ are consistent then $k_1^2 + k_2^2$ is equal to