find k which kx +y=k²and x+ky=1 have infinitely many solutions
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a1 = k a2 = 1
b1 = 1 b2 = k
c1 = k^2 c2 = 1
for infinitely many solutions
a1 / a2 = b1 / b2 = c1 / c2
k / 1 = 1 / k = k^2 / 1
Now ,
k / 1 = 1 / k
k^2 = 1
k = + 1 , -1
1 / k = k^2 / 1
k^3 = 1
k / 1 = k^2 / 1
k = 1
therefore ,
k = +1 and -1
b1 = 1 b2 = k
c1 = k^2 c2 = 1
for infinitely many solutions
a1 / a2 = b1 / b2 = c1 / c2
k / 1 = 1 / k = k^2 / 1
Now ,
k / 1 = 1 / k
k^2 = 1
k = + 1 , -1
1 / k = k^2 / 1
k^3 = 1
k / 1 = k^2 / 1
k = 1
therefore ,
k = +1 and -1
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This is the ans .
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