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Q.

If the system of linear equations 4x+ky+2z=0,kx+4y+z=0,2x+2y+z=0 possess  a non-zero solution, so that k has two values k1,k2then k13+k2333=

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answer is 2.6667.

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Detailed Solution

System has non-zero solution⇒Δ=0 ⇒4k2k41221=0 ⇒44-2-kk-2+22k-8=0 ⇒k2−6k+8=0 ⇒k=2,4 Let k1=2 and k2=4.  Then k13+k2333=8+6427=7227=2.6667
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